Add Doritos to a food processor and pulse until you have fine crumbs. Transfer to a bowl and set aside. Preheat oven to 375 degrees.
In a large bowl, add beef, egg, salt, pepper and 1/2 cup of the crushed Doritos. Mix until combined. Gather half the mixture into a ball and press into a large patty. Make a small indent in the center of the patty, add about 4 pieces of cheese and seal shut with more meat. Repeat with remaining meat. Lightly coat the patties with remaining Doritos crumbs.
Heat vegetable oil in a large nonstick skillet over medium heat. Add burger patties and cook until golden on both sides. Remove from pan, add to a baking sheet and bake for 10 minutes. Remove from oven and build burgers.