01 - Combine chickpeas and pressed tofu in a food processor; pulse until coarsely blended without pureeing.
02 - Transfer mixture to a large mixing bowl. Incorporate grated carrot, finely chopped onion, garlic, soy sauce, smoked paprika, thyme, black pepper, salt, olive oil, and breadcrumbs. Stir until thoroughly integrated.
03 - Divide the mixture evenly into 4 portions. Form each into a patty about 1/2 inch thick.
04 - Arrange flour on one plate, beaten eggs or aquafaba in a shallow bowl, and panko breadcrumbs on a separate plate.
05 - Coat each patty lightly with flour, then immerse in egg or aquafaba, and finish by pressing into panko breadcrumbs for a uniform crust.
06 - Heat 1 to 2 tablespoons olive oil in a large skillet over medium heat. Fry the patties for 4 to 5 minutes per side until golden and crispy.
07 - Lightly toast the burger buns for enhanced texture.
08 - Spread mayonnaise on toasted buns, layer lettuce, cooked patty, cheese slice, tomato, and pickles as preferred.
09 - Serve burgers immediately while patties remain hot and crisp.