Heat a medium saute pan over medium heat. Add 2 tablespoons oil and 1 cup onion. Reduce heat to medium-low, and cook, stirring occasionally, until onions are golden brown and caramelized, about 35 minutes. Set aside.
Soak bread in milk, flipping once. Finely chop. In a large bowl, combine the remaining 1/3 cup onions, the sirloin, garlic cloves, bread, egg, parsley, 2 teaspoons Worcestershire sauce, 2 teaspoons salt, and 1/4 teaspoon pepper. Mix with your hands to combine. Divide meat mixture into 6 oblong patties (about 5 inches long and 3/4 inch thick). Dust with cornstarch.
Heat a large skillet over medium-high heat. Add remaining oil, and reduce heat to medium. Cook patties, 3 at a time, for 6 minutes, without moving them. Flip, and cook until cooked through, about 9 minutes. Set aside on a plate. Repeat with remaining patties.
Make the gravy: Add cooked onions and 1 teaspoon cornstarch to same skillet, and stir for 1 minute. Raise heat to medium-high. Pour in broth and a dash of Worcestershire sauce, and whisk until broth is clear and slightly thickened, about 3 minutes. Remove pan from heat, and return patties and juices to skillet, spooning sauce on top.