In a mixing bowl, combine ground beef, bread crumbs, egg, salt, and pepper. Mix well.
Get at least 1/4 cup of the mixture. Roll into a ball then flatten using your clean hands. Set aside.
Heat cooking oil in a pan. Fry the patties until brown on both sides. Remove from the pan then drain excess oil.
Toast the burger buns if desired.
Spread some mayo-ketchup sauce in one half of the bun. Add one fried patty. Add cheese, onion, cucumber, and tomato slices if desired.
Put the other half of the bun on top then pierce with a toothpick to hold its form.
Repeat steps 5-6 for the remaining buns and patties.
Serve and enjoy your homemade burger!