Preheat your grill to medium-high heat and prepare for both indirect and direct cooking. 

Make the hamburger mixture. To a large bowl, add all of the burger patty ingredients.

Scoop up a couple of spoonfuls of the meat mixture and form into a patty, about the size of your palm. Place them on a baking sheet or platter to transport them outside to your grill. 

Grill burger patties over direct heat for 3-4 minutes per side, then transfer them to indirect heat. 

Carefully spoon 1 tablespoon of pizza sauce over each patty, then place a slice of cheese and pepperoni slices. 

Close the grill lid and allow the cheese to melt for 1-2 minutes. 

Carefully remove patties from the grill and transfer to a clean platter for serving. 

Prepare the buns: Melt butter, then brush on the inside of the hamburger bun halves.

Place the buns cut-side down on the grill over indirect heat for 1-2 minutes, until slightly toasted. 

Assemble burgers and serve warm.