Preheat oven to 350 degrees. Spray counter with non stick spray or add a little flour. Combine the thawed rolls into a ball and using a rolling pin, roll the dough into a 13-14 inch circle.
Place on a sprayed 12-14 inch pizza pan. Poke dough several times with a fork to prevent bubbles from forming. Pre bake pizza for 10 minutes.
While the pizza dough prebakes start on the apple filling. Peel and dice the apples small and place in a large skillet.
In a small bowl combine the sugar, brown sugar, cinnamon, and corn starch. Add 1 tablespoon of butter. Sprinkle the dry ingredients over the apple and add the water and vanilla extract.
Cover and bring mixture to a slow boil, turn the heat down to low and simmer (stirring occasionally) until the apples are tender and the mixture starts to thicken. Remove from heat and set aside to slightly cool.
Remove the pizza dough from the oven and set aside. Spread the apple pie filling evenly over the pizza crust.
To make the buttery crumb topping, in a small bowl combine the flour, sugar and butter. Use a fork or pastry blender and cut in the flour until it resembles crumbs.
Sprinkle the topping evenly over the apple pie filling. Bake 20 - 25 minutes or until the crust and topping are golden brown.
Remove from oven, cool slightly and drizzle melted caramel over the pizza before slicing and serving.