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1
Whisk 1 1/8 cups flour, white sugar, and salt together in a bowl. Press 1/2 cup butter pieces into flour mixture with your fingers until the mixture resembles coarse crumbs.
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2
Make a well in the center of the flour mixture. Pour water and vanilla into well; quickly work water and vanilla into flour to create a loose dough, adding more water if the dough is crumbly. You should be able to squeeze it in your hand and have it stay together but be a bit crumbly. Shape dough into a flat disc, wrap in plastic wrap, and refrigerate for at least 30 minutes.
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3
Stir brown sugar, 1 tablespoon flour, and cinnamon together in a bowl. Add apples and toss to coat. Let sit for flavors to blend, about 10 minutes.
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4
Preheat oven to 450 degrees F (230 degrees C).
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5
Roll dough out into a large, rough circle on a baking stone or baking sheet. Pour apple mixture into the center of the dough, leaving a 2-inch uncovered border, and dot apples with 1 tablespoon butter.
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6
Fold edges of dough up over the apples, leaving an opening in the center. Dot dough with remaining 1 tablespoon butter and sprinkle coarse sugar over the dough.
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7
Bake in the preheated oven until the crust is crisp and golden and apples are tender and caramelized, 40 to 45 minutes.
