Preheat an outdoor grill for medium-high heat and lightly oil the grate.
Mix ground beef, egg, onion, and chopped mushrooms together in a bowl, seasoning with pepper, garlic salt, and salt as you mix. Form mixture into patties about 2 inches in diameter.
Grill patties on the preheated grill until browned and desired doneness is reached, 5 to 7 minutes per side. An instant-read thermometer inserted into the center should read at least 160 degrees F (70 degrees C).
Grill portobello mushrooms, green bell pepper, red bell pepper, and yellow bell pepper on the grill until tender, 3 to 5 minutes per side. Use 2 mushrooms and as the 'bun' for the burgers.