Preheat oven to 375 degrees. Place foil on bottom oven rack to catch any juices.
On a lightly floured work surface, roll out one disc of dough to 1/8 inch thick. Cut out an 11-inch round, and fit into a 9-inch pie plate. Refrigerate crust while you prepare the lattice strips.
On a lightly floured piece of parchment, roll out second disc of dough to 1/8 inch thick. Trim to make a 9-by-12-inch rectangle. Using a clean ruler as a guide, cut 16 strips (each 12 inches long and 1/2 inch wide) with a fluted pastry wheel or a sharp knife. Place strips on a parchment-lined baking sheet, and refrigerate until cold, about 10 minutes.
Combine sugar, cornstarch, salt, and cinnamon in a large bowl. Using your fingertips, rub vanilla seeds into sugar mixture. Add cherries, and toss. Pour cherry mixture into prepared pie plate. Dot top with butter. Lightly brush exposed edge of crust with egg.
Make the lattice: Lay 8 strips of dough across pie. Fold back every other strip. Lay another strip perpendicular in center of pie. Unfold the strips over perpendicular strip. Fold back the strips that are under the perpendicular strip. Lay a second perpendicular strip next to the first. Unfold the strips over the second perpendicular strip. Repeat, weaving strips across half the pie. Return to center, lay a perpendicular strip on unwoven side of pie, and repeat. Trim strips to make a 1-inch overhang. Tuck extra under rim of crust, and crimp to seal. Brush lattice with egg.
Bake until crust is golden brown and juices are bubbling (if using fresh cherries, begin checking after 1 hour; if using frozen, it will take about 1 hour, 35 minutes). If top begins to brown too quickly, tent with foil and continue to cook.
Let pie cool slightly on a wire rack. Meanwhile, warm jam in a saucepan over medium heat, then pass through a sieve. Brush warm pie with jam, then let cool.
Pie can be stored at room temperature (covered loosely with parchment and tented with foil) for up to 1 day.