Step 1

To make the crust, mix flour, sugar, salt, and butter on medium speed until mixture resembles coarse sand. Add the yolks; mix slightly. Add ice water. Mix until just combined. Form dough into disk; wrap in plastic. Chill for 1 hour or up to 3 days.

Step 2

To make the filling, melt butter in a large pan on high heat. Add apples, zests, and salt, stirring until coated. Sprinkle sugar, and saute, stirring, until sugar is dissolved, liquid has thickened, and apples are almost golden, about 5 minutes. Transfer to a baking sheet, and let cool to room temperature.

Step 3

To make the crumb topping, combine flour, dark-brown sugar, granulated sugar, salt, cinnamon, allspice, and butter in a food processor, and pulse until mixture resembles coarse sand. Refrigerate until ready to use.

Step 4

To assemble, preheat oven to 375 degrees and flour a piece of parchment paper. Roll chilled dough into a 1/4-inch-thick, 14-inch circle on parchment (trim excess). Place dough and parchment on cookie sheet. Mound cooled apple mixture in center, leaving a 3-inch border. Sprinkle crumb mixture on top of apples. Fold edges of the dough on top of apples, overlapping and leaving about a 6-inch round opening. Refrigerate until dough is firm, about 30 minutes. Brush edge of crust with egg, and sprinkle with sugar. Bake until pastry is golden brown and apples are tender, about 40 to 50 minutes. Serve warm or at room temperature, with vanilla ice cream.