Prepare a grill fire to 400° with a pizza stone over indirect fire. Use pecan chunks if you would like to add smoke flavor. Cool down to 350° for cooking.
Slice apples thin, a mandoline works great for this.
In a small bowl combine brown sugar with cinnamon.
Add apples to a large bowl with half of the cinnamon sugar. Mix to combine. Set aside while you prepare the dough.
Roll pizza dough out into a 8 inch circle on a floured surface.
Spread softened butter over pizza crust.
Sprinkle cornmeal onto a pizza peel.
Place dough onto peel. Fold up the edges slightly to create an edge.
Sprinkle cinnamon sugar over butter, reserving one tablespoon for the top of the apples.
Layer sliced apples over the cinnamon sugar.
Drizzle about 1 - 2 tablespoons of juice from the apples over the apple slices.
Sprinkle with remaining cinnamon sugar.
Sprinkle pizza stone with cornmeal.
Carefully slide the pizza onto the stone and cook with the grill lid closed about 5 minutes. Using a large spatula, turn pizza a quarter turn about every 5 minutes, cooking with the lid closed until pizza crust is crisp. Total cooking time will be about 20 minutes.
Remove from grill to a cutting board. Slice and serve warm or at room temperature.