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1
In a medium saucepan, bring the maple syrup to a boil over medium-high heat. Decrease the heat to medium-low and simmer for 15 to 25 minutes, or until thickened, dark, and reduced to about 1/4 cup (60 milliliters). (It foams up in the pan, so be sure to use a large enough pan so it doesn't boil over. Once it foams, turn down the heat so it simply simmers-if it keeps foaming it will start to burn. Watch it carefully! It will look like it's boiling away, so keep decreasing the heat to keep it at a low simmer.)
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2
Remove from the heat and whisk in the butter. Pour the maple butter into a 9-inch (23-centimeter) round cake pan. It may harden into a firm mass-do your best to spread it evenly on the bottom of the pan, but don't stress about it.
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3
Place a rack in the center of the oven and preheat to 350u00b0 F (175u00b0C).
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4
Place the pears, rounded side down, in the caramel in the cake pan, as close together as possible and overlapping them a bit to cover the entire bottom of the pan. You want every single possible bottom surface of the pan to be covered with pears; the fruit cooks down and reduces somewhat in the oven, so don't be shy about packing the fruit in tightly. When you have covered the bottom layer as best you can, cut any remaining pear halves in quarters or eighths so you can better layer the pears on top of each other, arranging the fruit so that it is fairly level on top.
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5
Remove the dough circle from the refrigerator and trim it so that it is an even circle, keeping it about 10 inches (25 centimeters) in diameter. Drape the dough directly on top of the pears and tuck the edges of the dough around the fruit into the sides of the pan. Bake for 70 to 80 minutes, or until the puff pastry is deep golden brown and the juices from the pears are bubbling up along the sides of the pan.
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6
Place a large serving platter on top of the tart and quickly and carefully invert the pan so the puff pastry circle is on the bottom and the fruit is on top. Rearrange the fruit, if necessary, as sometimes it gets jostled loose and falls off the pastry. Serve warm or at room temperature with creme fraiche or unsweetened whipped cream. The tart can be stored in an airtight container at room temperature for up to 3 days.
