Finely chop the onion and carrot.
Mix the chopped vegetables, salt, and pepper with ground beef.
Shape the mixture into round, flat patties like tteokgalbi.
Heat a pan with oil and cook the patties until browned on both sides.
Place lettuce and tomato slices on whole wheat bread.
Add the cooked tteokgalbi patty and drizzle with low-sugar ketchup.
Top with another slice of bread to complete the sandwich.