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1
To make the crust: Put the yeast, 1 teaspoon of the sugar, and 1/4 cup of the warm water (check the yeast package for the correct temperature) in a small bowl. Stir and let stand for about 5 minutes, or until the yeast dissolves and becomes creamy. The mixture may or may not bubble.
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2
Put the all-purpose, whole wheat, and rye flours, along with the remaining 1 teaspoon sugar and the salt, in the bowl of a stand mixer fitted with the paddle attachment. (Alternatively, you can make this dough in a bowl with a wooden spoon.) Turn the mixer to low and beat just to blend the dry ingredients. Pour in the yeast mixture and continue to mix for a minute or two; the dough will be dry and shaggy, but that's fine. Mix the olive oil with the remaining 1/4 cup warm water, pour it into the bowl and mix at medium speed. The dough will quickly absorb the liquid and, in a minute or so, start to ball up around the paddle and slap the sides of the bowl. If the dough looks dry and doesn't come together, add some more water, a teaspoonful at a time. Depending on your flour (and the day), the dough might need just a splash or a couple of teaspoons water. Keep the mixer at medium speed and beat the dough for 5 minutes. (If you're working by hand, turn the dough out onto a lightly floured work surface and knead the dough until it is smooth.) You'll have a springy, slightly sticky dough.
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3
Shape the dough into a ball, place it in a clean bowl and cover the bowl tightly with plastic film. Put the bowl in a warm spot (between 70u00b0 and 75u00b0 F) and allow the dough to rise until doubled in volume, 2 to 2 1/2 hours.
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4
Position a rack in the lower third of the oven and remove any higher racks; you'll need room to get the tarte flambee in and out quickly. If you've got a pizza or bread stone, put it on the rack; if not, put a heavy cookie sheet on the rack (or, in a pinch, flip over a rimmed baking sheet). Preheat the oven to its highest setting, as close to 600u00b0 F as you can get. After the temperature indicator goes off, keep preheating for another 20 minutes -- remember, you've got to heat the stone as well as the oven. If you've got a pizza peel, have it at the ready; a rimless cookie sheet makes a good stand-in.
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5
Meanwhile, make the topping: Whisk all of the ingredients (except the apples) together in a medium bowl until smooth. Cover until needed.
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6
Turn the dough out onto a floured work surface and press it down with your palms. Lightly flour the top of the dough and start rolling it out. You can roll the dough into a rectangle, a circle, or something more free-form. Rolling a springy yeast dough like this isn't easy, and so I'm content to go with whatever shape I end up with; the shape is less important than the thinness. You want to roll the dough as thin as you possibly can and, to get it to behave and thin out, you might have to roll, let it rest for a few minutes, roll and rest again. Relax, and the dough will too. Each time you let the dough rest, cover it with plastic film or a kitchen towel.
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7
Lightly flour the preheated peel or rimless cookie sheet and transfer the dough to it. (I roll the dough up around my floured rolling pin and then unroll it onto the peel.) Brush off any excess flour and use a fork to prick the dough all over -- really, all over. You want to make sure you prick the dough all the way through, so listen for the rat-a-tat of the fork against the peel.
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8
Slide the baking stone into the oven, shut the oven door and set a timer for 1 minute. When the timer rings, pull out the tart. Depending on what kind of work surface you have, you can either put the hot tart on the counter or slide it onto a cooling rack. Using a flexible spatula or a large spoon, spread the topping over the crust, going very close to the edges.
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9
Cut a small slice off two opposite sides of each apple to expose the flesh and then slice each apple, from top to bottom, paper-thin on a mandolin or Benriner until you've almost reached the core on the first side of the apple. (If you don't have a mandoline, cut the apples in half from top to bottom and slice them with a thin blade on a food processor, or do this by hand.) Turn the apple to the opposite side and slice almost to the core. (The leftover piece encasing the core is the baker's nibble.) Arrange the apple slices in a single layer over the cream topping. Sprinkle generously with sugar or cinnamon sugar.
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10
Slide the tart back onto the baking stone and bake for about 5 minutes more. You want the crust to be dark and well baked on the bottom, and if you've got a burnt edge here or there and the occasional curled and browned apple slice, so much the better. Transfer the tart to a cutting board, immediately cut it with a pizza wheel or chef 's knife and serve.
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11
Serving: Just like pizza, tarte flambee is meant to be eaten seconds out of the oven. At Flamme & Co, the dessert is served with a fork and knife (the way just about everything is served in France), but chez you, it's fine to pick it up and eat it out of hand -- it's what we do chez moi.
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12
Storing: Once made, the tart has to be eaten immediately. You can make the dough a day ahead, let it rise, flatten it and put it in the refrigerator. Keep flattening it as it rises and then, when it's worn itself out (usually in an hour or two), wrap it tightly in plastic film and keep it cold. When you're ready to make the tart, take the dough out of the refrigerator, put it in a covered bowl in a warm place and allow it to rise to double its size again.
