MAKE glaze: Put reserved peels and cores in a large saucepan, along with sugar. Pour in just enough water to cover; simmer for 25 minutes or longer. Strain.

MAKE DOUGH: MIX flour, sugar, and salt in a large bowl; add 2 tablespoons of the butter. Blend in a mixer until dough resembles coarse cornmeal. Add remaining butter; mix until biggest pieces look like large peas. (I just cut the butter in with pastry blender all at once.)

DRIBBLE in water, stir, dribble in more, until dough just holds together. Toss with hands, until its ropy with some dry patches. If dry patches predominate, add another tablespoon water. Keep tossing until you can roll dough into a ball. Flatten into a 4-inch-thick disk, wrap in plastic wrap; refrigerate at least 30 minutes.

REMOVE dough from fridge; let soften so malleable but still cold. Smooth cracks at edges. On a lightly floured surface, roll into a 14-inch circle about 1/8 inch thick. Dust excess flour from both sides with a dry pastry brush. (I rolled out dough between folded plastic wrap.) PLACE dough on a parchment-lined baking sheet. Heat oven to 400 F.

Leaving a 2 to 3 margin from edge, overlap apples on dough in a ring until you reach the center. Fold edges of dough back onto itself; crimp edges at 1 intervals.

BRUSH butter over apples and dough edge. Sprinkle 2 tablespoons sugar over dough edge and the other 3 tablespoons over apples. (This was a lot. I used about 3 T.)

BAKE in center of oven until apples are soft, and crust has caramelized to a dark golden brown (about 45 min), making sure to rotate tart every 15 minutes.

REMOVE tart from oven, and slide off parchment onto cooling rack. Let cool at least 15 minutes. BRUSH glaze over tart, slice, and serve.