Place 6 slices of bread onto a baking sheet. Spread a small handful of the mozzarella cheese over each slice. Top with the remaining 6 slices of bread. Mix together the butter and garlic powder, brush some over the tops of the sandwiches, or spread with the back of a tablespoon. Sprinkle with dried oregano.
Place baking sheet under the broiler for 2 to 3 minutes, until golden brown. Remove pan from oven, flip sandwiches, and brush the other sides with butter, and sprinkle with oregano. Return to the broiler, and cook until golden, about 2 minutes.
Cut sandwiches in half diagonally, and serve immediately with vodka sauce on the side for dipping.