Preheat oven to 350 degrees F (175 degrees C). Grease a fluted tube pan (such as Bundt(R)) with cooking spray.
Mix olive oil, Italian dressing mix, and garlic together in a large bowl.
Flatten each dough piece with your fingers. Add 3 pieces of pepperoni and 2 cubes of mozzarella cheese; wrap dough around filling to form a ball. Transfer to the bowl with the olive oil mixture; mix until coated.
Arrange half of the dough balls around the bottom of the tube pan. Scatter pepperoni and mozzarella on top. Top with remaining dough balls. Sprinkle Parmesan cheese and oregano on top. Cover with aluminum foil.
Bake in the preheated oven until cheese melts, about 15 minutes. Uncover and continue baking until golden brown, 10 to 15 minutes. Cool in the pan for 5 minutes. Invert onto a serving plate.