1. In a bowl, mix cherries, 1 1/4 cups sugar, tapioca and vanilla. Let stand for 15 minutes, stirring occasionally. Preheat oven to 375ºF. Line a rimmed baking sheet with foil and place in lower third of oven.
2. Unroll one pie crust; transfer to a 9-inch pie plate. Pour in filling. Unroll second crust and cut into 3/4-inch strips with a sharp knife. Place half of dough strips across pie, spacing evenly. Arrange remaining strips in opposite direction atop first, lifting strips and weaving to form a lattice. Press ends to edge of bottom crust; trim overhang. In a bowl, whisk egg with 1 tsp. water. Brush over crust; sprinkle with remaining 1 tsp. sugar. Place pie on baking sheet in oven and bake until crust is golden brown and filling is bubbling, about 1 hour.
3. Remove pie from baking sheet. Place on a wire rack to cool for at least 1 hour before slicing and serving.