Place beef and bacon into a large mixing bowl and season with salt and pepper. Mix together until fully combined.
Form six equal patties and place in the refrigerator between parchment to chill.
Heat a grill pan over medium-high heat and brush the surface with vegetable oil.
Place patties onto the grill pan (three at a time) and grill for 5 to 7 minutes on each side.
About two minutes before the patties are done, place a piece of cheddar and jack cheese over each patty and allow cheese to melt before removing and placing onto a clean surface. Repeat with the remaining patties and cheese.
To assemble: Stack two patties onto one another and place on a bun. Add any remaining toppings and condiments of your choice and serve.