In a large bowl, combine the ground beef, cheddar cheese, breadcrumbs, egg, Worcestershire sauce, garlic powder, onion powder, salt, and pepper. Mix until just combined, being careful not to overwork the meat.
Divide the mixture into four equal portions and shape them into patties. Make a slight indentation in the center of each patty to prevent them from puffing up while cooking.
Heat olive oil in a skillet over medium-high heat. Cook the patties for about 5-6 minutes on each side, or until they reach your desired level of doneness. During the last minute of cooking, place the burger buns cut-side down in the skillet to toast.
Assemble the burgers by spreading mayonnaise on the bottom bun, followed by the lettuce, burger patty, avocado slices, and tomato. Top with the other half of the bun and serve immediately.