Preheat the oven to 400 degrees F. If grilling the pie, see grilling note below.
In a large bowl, toss the cherries with the sugar, cornstarch, vanilla and almond extract until coated. Set aside.
Remove one of the pie crusts from its package and using a rolling pin, roll it out gently to form a 12-inch circle. Place the pie crust in the bottom of a 10-inch cast iron skillet that has been sprayed with cooking spray. Pour the berry mixture into the skillet and dot with pieces of the butter.
Next, take the other pie crust and roll it out to a 12-inch circle. Cut the pie crust into strips about ¾" wide or so that you have 9-10 strips. Lay 5 strips along the top of the pie, with the longest strip in the middle. Lay the rest of the strips evenly across the first set of strips, weaving the strips to create a lattice effect. Tuck the edges of the strips into the bottom pie crust and gently crimp the edges.
Mix the egg and cream in a small bowl and brush it on the pie crust strips then sprinkle with the coarse sugar. Bake the pie for 40 minutes or until the crust is golden and the filling is bubbly. Let the pie cool completely to set the filling. If the filling is too runny, refrigerate for ½ hour or longer to set.
GRILLING NOTE: To grill the pie, preheat half of the grill to medium and then place the skillet on the grill rack over the empty side of the grill. Cover and grill for 1 ½ to 2 hours or until the crust is golden and filling is bubbly, rotating once halfway through grilling time.