Preheat the oven to 425°F.
Dust a large cutting board or countertop with all-purpose flour. Place the pizza dough on the surface and roll it out until it is about 1/4 inch thick. Set aside.
In a medium bowl, combine the pudding mix, all-purpose flour, chilled and cubed butter, granulated sugar, brown sugar, and a pinch of salt. Mix together until it forms a thick paste.
Spread the pudding mixture evenly over the pizza dough. Roll up the edges to form a crust.
Bake for about 15 minutes or until the crust is golden brown. Allow pizza to cool before slicing.
Once cooled, slice into desired slices.