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To make the tart dough: Put the flour, salt, and sugar into the bowl of a food processor fitted with the metal blade.
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Process for a few seconds to mix the dry ingredients.
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Drop the cut-up butter on top of the flour, and pulse the machine in a dozen or more short bursts, until the mixture is crumbly, with only small bits of butter visible.
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Pour the egg yolks over the crumbs, and pulse in bursts, about 5 seconds total, to moisten the dough.
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Scrape down the sides of the bowl, sprinkle 2 tablespoons of ice water on the dough, and pulse again for a few seconds.
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The dough should begin to clump together but not form a solid mass.
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Scrape it all out onto a board or into a large bowl; gather and press the clumps into a firm ball that holds together.
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If it crumbles apart, sprinkle more ice water over the dough and knead gently.
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When the dough sticks together, flatten it into a disk, wrap well in plastic, and refrigerate for 6 hours or up to a day before rolling.
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Freeze the dough for longer keeping.
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To make the filling: Put the sugar, the lemon zest and juice, and the butter in the heavy pan.
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Spread the sugar around the pan bottom.
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Cut the pears in half, and neatly pare away the cores and stems.
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Lay the halves in one layer on top of the sugar in the pan, cut side down.
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Set the pan over medium heat, and let the sugar and butter melt and form a syrup with the juices released by the fruit.
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As it heats, spoon the syrup over the skins of the pear halves.
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When the syrup starts to boil, adjust the heat to maintain a bubbling simmer, and cook, still cut side down, for about 10 minutes.
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Carefully turn the pears over, and simmer them for 15 minutes on the skin side.
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Turn them to cook once again on the cut side for another 10 minutes or more, until they are cooked througheasily pierced with the tines of a fork, and very soft to the touch.
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(If you are using small Seckel pears, turn them sooner and expect shorter total cooking time.)
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Remove the pan from the heat, and let the pears cool completely in the syrup.
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Make sure they are cut side down, so they become saturated.
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(Steep them in the syrup overnight, refrigerated, if you like.)
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When you are ready to roll out the pastry and assemble the tart, lift the pear halves and drain all the syrup back into the pan.
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Set the pears on paper towels to dry the cut sides.
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Place the pan with all the residual syrup over medium-high heat, bring to a boil, and cook it rapidly, until it reduces and just begins to caramelize.
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Lower the heat, and when the syrup turns deep gold, pour it into a heat-proof cup.
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Heat the oven to 350 , with a rack set in the center.
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Place a baking stone on the rack if you have one.
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To form the tart shell: Cut off a third of the sweet dough in a single piece for lattice top.
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Keep it chilled.
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Place the larger piece of dough between two large sheets of parchment, and roll it out to an even 12-inch round.
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Peel off the top sheet of parchment, invert the dough circle over the tart pan, and peel off the remaining sheet.
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Press the dough gently down into the pan so it covers the bottom and lines the sides.
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Trim the edges of the dough round so it is even with the pan rim.
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With your fingers, form an even wall all the way around.
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Use scraps of dough to fill cracks or thin spots on the bottom or sides.
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Now roll the smaller piece of dough between the parchment sheets to an 11-inch round.
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Remove the top parchment sheet, and cut the dough in 1-inch-wide strips with a pastry cutter or sharp knife.
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Leave the strips in place on the parchment sheet (and, if your kitchen is warm, refrigerate them) until you are ready to form the lattice.
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Spread the apricot jam to cover the bottom of the tart crust.
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Place the pear halves in the crust, skin side up, in one layer.
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Drizzle the golden pear syrup all over the fruit.
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Form the lattice top, first laying half the strips over the pears, parallel and spaced about an inch apart.
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Lay the other half of the strips at an angle, covering the whole tart in an even pattern.
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Press and pinch the ends of the strips neatly into the rim of dough in the pan.
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Finally, brush the lattice strips with the egg-yolk glaze.
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Bake the tarton the stone if you have onefor about 40 minutes, or until the lattice is deep golden brown and the exposed pear tops are lightly caramelized.
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Cool the tart on a wire rack.
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When the crust has cooled a bit and contracted, slip off the fluted side ring.
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Serve warm or at room temperature, cut in wedgeswith your favorite kind of cream.
