On a lightly floured surface, roll half the chilled dough into a 12-inch circle. Carefully transfer it to a 9-inch pie dish, easing it into corners without stretching. Trim the edges to a 1-inch overhang, fold under to reinforce, and flute. Chill the crust in the freezer for 20 minutes while heating the oven to 400°F (205°C).
Line chilled crust with parchment and fill with pie weights. Bake on the lower rack for 18-20 minutes, until the edges are just golden and the bottom looks dry. Lift out the weights and parchment. Return crust to oven for 5-7 more minutes to set a crisp base. Cool to room temperature before filling.
Place cherries in a fine strainer set over a bowl and let them drain for 20-30 minutes if very juicy. In a large bowl, toss cherries with sugar, tapioca, cornstarch, salt, lemon juice, and almond extract. Let mixture stand 15 minutes, gently stirring once or twice, until fruit glistens and juices begin to thicken slightly.
Roll out remaining dough on a floured surface into a rectangle about 1/8-inch thick. Using a sharp knife or pastry wheel, cut into 10-12 even strips, about 3/4- to 1-inch wide. Transfer to a parchment-lined baking sheet, cover, and refrigerate until firm, at least 15 minutes.
Stir drained cherries; spread the mixture and accumulated juices evenly in the cooled crust. Dot the fruit with butter cubes. Lay 5-6 strips evenly spaced over the filling, then weave in remaining strips to form a lattice. Trim any overhanging strips and press ends into the edge. Chill assembled pie for 15 minutes.
Beat egg and cream together for egg wash. Brush lattice and edge generously, then sprinkle with coarse sugar. Set pie on a parchment-lined baking sheet and bake at 400°F (205°C) for 20 minutes. Reduce heat to 350°F (175°C) and continue baking 50-60 minutes, rotating halfway, until filling is bubbling thickly through the lattice and crust is rich golden brown.
Place baked pie on a rack and cool at least 4 hours so juices set; the filling should be thick, jewel-like, and not run when sliced. Don’t cover during this stage. Once cool, slice with a sharp knife for clean wedges and serve at room temperature.
