1. In a mixing bowl, combine crumbled tofu, grated carrot, soy sauce, sesame oil, panko breadcrumbs, and beaten egg. Mix well until all ingredients are combined.
2. Form the mixture into 4 equal-sized patties.
3. Heat vegetable oil in a frying pan over medium heat. Cook the patties for about 5-7 minutes on each side, or until golden brown and cooked through.
4. Serve the tofu burgers on buns with your favorite toppings and condiments.