Classic Sour Cherry Pie With Lattice Crust

Name: Classic Sour Cherry Pie With Lattice Crust
Ingredients: 2 1/2 cups unbleached all purpose flour; 1 tablespoon sugar; 3/4 teaspoon salt; 1 cup (2 sticks) chilled unsalted butter, cut into 1/2-inch cubes; 5 tablespoons (or more) ice water; 1 cup plus 1 tablespoon sugar; 3 tablespoons cornstarch; 1/4 teaspoon salt; 5 cups whole pitted sour cherries or dark sweet cherries (about 2 pounds whole unpitted cherries); 1 teaspoon fresh lemon juice (if using sour cherries) or 3 tablespoons fresh lemon juice (if using dark sweet cherries); 1/2 teaspoon vanilla extract; 2 tablespoons (1/4 stick) unsalted butter, cut into 1/2-inch cubes; 1 tablespoon (about) milk; Vanilla ice cream