Preheat the oven to 180C/350F.
In a non-stick pan or skillet, add the butter and place over medium heat. Once hot, add the sliced sirloin steak and season with salt and pepper. Cook the steak until no longer pink. Remove the steak from the skillet.
Add the bell peppers, onion, and garlic and cook for 4-5 minutes, until they soften. Add the cream cheese and half-and-half and mix well. Bring everything to a simmer and cook for a further 5 minutes.
Add the steak back into the pan, along with half the cheddar cheese and half the pepper jack cheese, and mix well.
Transfer the cheesesteak mixture into a greased 9 x 13-inch baking dish. Sprinkle with remaining shredded cheese and bake for 15-20 minutes or until the cheese is bubbling and golden.