Knead together the ground beef, egg, bread crumbs, milk, and spices. Form into 4 burger patties. Heat a cast iron skillet medium/hot and melt the butter. Place the burgers on the skillet so they sear and create a crust. After about 3–4 minutes, flip the burger to create the crust on the other side. Cook the burger a little bit rarer than your preference as they will cook some more in the oven. Place burgers on a baking sheet. Put 1–1/2 tablespoons of pizza sauce on each burger. Sprinkle grated mozzarella on top of the pizza sauce. Place 6 pepperoni slices on each burger. Broil the burgers at 450 degrees for 5 minutes or until the cheese is melting. Serve on a toasted bun.