Dominican Chimichurri Burgers

1 1/4 pound ground beef chuck
1 medium onion, finely chopped
1/2 large red bell pepper, diced
2 garlic cloves, minced
1/3 cup chopped cilantro
1 teaspoon dried oregano
2 teaspoons soy sauce
1 tablespoon Worcestershire sauce
4 hamburger buns, split
2 cups thinly sliced cabbage
1 carrot, coarsely grated
1 small red onion, cut into rings
1 tomato, sliced 1/4 inch thick
2 tablespoons ketchup
2 tablespoons mayonnaise
1 tablespoon yellow mustard

Mix together beef, onion, bell pepper, garlic, cilantro, oregano, soy sauce, Worcestershire sauce, a scant 1/2 teaspoon salt, and 1/2 teaspoon pepper. Form into 4 (4 1/2-inch-wide) patties.
Heat a large griddle or 12-inch heavy skillet over medium heat until hot, then lightly toast buns.
Oil griddle, then cook patties, turning once, about 8 minutes total for medium-rare. Transfer to buns.
Mix together cabbage, carrot, and 1/4 teaspoon salt, then cook, turning occasionally, until slightly wilted, about 2 minutes. Divide among burgers.
Oil griddle again, then sear onion and tomato, turning once, until slightly charred, about 2 minutes total. Divide among burgers.
Stir together ketchup, mayonnaise, and mustard, then top burgers with sauce.