Whisk the flour, sugar, and salt in a large bowl. Cut in the cold butter until the pieces are pea-sized. Sprinkle in the ice water one tablespoon at a time, tossing gently until the dough holds together when squeezed. Divide the dough in half, shape into disks, wrap, and refrigerate for 30 minutes.

Heat the oven to 350°F. Place one rack in the middle and one on the bottom. Line a baking sheet with foil on the bottom rack.

Roll one disk of dough into a 12-inch circle. Fit it into a 9-inch pie plate and refrigerate while making the filling.

Crush half a cup of gooseberries in a saucepan, stir in sugar, tapioca, and salt. Cook over medium heat until it boils. Boil for 2 minutes, then remove from heat and add remaining berries.

Pour the filling into the bottom crust. Roll the second disk and place it over the top, or cut into strips for a lattice top. Trim edges, crimp, and cut steam slits.

Brush the top with milk and sprinkle coarse sugar. Bake for 35-45 minutes until the crust is golden brown and filling bubbles. Cool on a wire rack for at least 20 minutes before slicing.