Preheat the oven to 375˚F.
Divide the dough in half and on a lightly floured surface, roll each piece into a 10-inch square.
In a small dish, stir together the oil and Italian seasoning or thyme.
Brush each square with oil and top with grated cheese and sliced pepperoni or ham.
Roll up as if you were making cinnamon buns, cut in half crosswise and each half in quarters so that each roll makes 8 pieces.
Place in four rows of four in a parchment-lined 9x9-inch pan and brush the tops with any remaining oil in the bowl.
Bake for 25 minutes, or until puffed and golden.