Adapted from Food You Want for the Life You Crave
Preheat an outdoor grill or indoor broiler.
Caramelize the vegetables: Heat the olive oil in a large skillet over medium heat. Add the chopped veggies, starting with the firmer ones first and adding the softer ones 5 or 6 minutes later. Cook, stirring frequently, until they are a rich brown in color and soft in texture, 10 to 15 minutes total. Allow to cool slightly.
In a large bowl, mix the beef, vegetables, onion, eggs, tamari, sriracha, mustard, salt, and pepper.
Divide the mixture into 8 round patties, and flatten them just slightly.
Arrange the burgers on the grill grate or in a greased broiler pan, and cook until lightly browned on the first side, 7 to 9 minutes. Flip the patties and cook for 4 to 6 minutes more, or until cooked to medium (with a light pink center).
Serve, if desired, on buns or lettuce leaves, with Sriracha Mayo, sliced red onion, sliced tomatoes, and, yup, ketchup, if you like.