Combine the ground beef, onion, garlic, breadcrumbs, salt, pepper, and egg; mix until thoroughly combined.
Divide the mixture into four equal portions; shape into a patty about 4 inches wide.
Preheat a gas grill to 400˚F.
Arrange the burgers on the grill, and press down the center of each patty with your thumb to make an indentation. Close the lid.
Cook the burgers, turning once, until browned on both sides and no longer pink inside, about 10 minutes.
Top each patty with 1 slice of cheese and continue to cook for 1 minute or until the cheese begins to melt.
Remove from grill and set aside to rest for at least 5 minutes.
Meanwhile, arrange the buns, cut side down, on the grill, and cook until lightly toasted, about 1 minute.
Spread mayonnaise and ketchup on the bottom bun.
Add the remaining cheese slices over the mayo and ketchup. Then, add lettuce, tomato, the burger patty, and sliced red onion.
Top with a bun and serve.
Notes
Mix Gently: Combine the meat with the ingredients until just mixed to avoid tough burgers.
Indent Patties: Press down the center of the patties before grilling to prevent puffing.
Minimal Flipping: Flip burgers only once on the grill to retain juices.
Meat Thermometer: Use a thermometer to check for doneness; aim for 160°F to 165°F for safety. Though I advise against it (ground beef is not a steak), if you'd like a medium-done burger, aim for 140 to 145˚F.
Rest Before Serving: Let burgers rest for at least 5 minutes post-cooking for juicier results.