1 1/4 cups all purpose flour
1/2 tablespoon sugar
1/2 teaspoon salt
1/2 cup (1 stick) chilled unsalted butter, cut into 1-inch pieces
4 tablespoons (about) ice water
Blend flour, sugar and salt in processor. Add butter; cut in using on/off turns until butter is cut into 1/4-inch pieces. Add 3 tablespoons water and blend until moist clumps form, adding more water by tablespoonfuls if dough is dry. Gather dough into ball. Flatten piece into disk; wrap in plastic. Chill at least 30 minutes. (Can be prepared 1 day ahead. Keep refrigerated. Let soften slightly at room temperature before rolling out.)
1/2 cup sugar
2 tablespoons all purpose flour
1/4 teaspoon ground allspice
1 3/4 pounds apples, peeled, quartered, cored, thinly sliced .
1 tbsp vanilla extract
Combine sugar, flour and allspice in large bowl. Mix in apples, then vanilla extract.
1/2 cup all-purpose flour
1/2 cup firmly packed light brown sugar
1/4 tsp ground cinnamon
5 tbsp (2.5 oz) unsalted butter, chilled
Combine the flour, brown sugar, and cinnamon in the work bowl of a food processor fitted with the steel blade. Cut the butter into small pieces and add to the dry ingredients. Pulse until the butter is cut into very small pieces, 30 seconds to 1 minute.
When you're ready to start putting it all together, position rack in bottom third of the oven and preheat to 375F.
Bake pie until apples are tender and topping is light golden, about 45-50 minutes. Transfer to rack. Serve pie warm or at room temperature with vanilla ice cream.