Garlic-Teriyaki Egg Burgers with Caramelized Onions

Ingredients

Caramelized Onions:
2 tablespoons butter
1 large sweet onion, thinly sliced
Teriyaki Sauce:
¼ cup soy sauce
1 tablespoon dark brown sugar
Patties:
2 lbs. ground chuck
3 cloves garlic, peeled and minced
½ teaspoon black pepper
vegetable oil, for brushing the grill rack
6 slices cheddar cheese
2 tablespoons butter
6 large eggs
6 hamburger (egg) buns, split
Japanese-Style Mayonnaise:
2 tablespoons mayonnaise
½ teaspoon seasoned rice wine vinegar

Instructions

Prepare a medium-hot fire in a charcoal grill with a cover, or preheat a gas grill to medium-high. To make the caramelized onions, melt two tablespoons of butter in a small sauté pan placed on the grill rack. When melted, add the onions and stir to coat the pieces with butter. Cook the onions, stirring occasionally, until golden brown and caramelized, about 15 minutes. Set aside. To make the teriyaki sauce, combine the soy sauce and brown sugar in a small bowl and set aside. To make the patties, combine the ground chuck, four tablespoons of the teriyaki sauce, the garlic and the pepper in a large bowl. Handling the meat as little as possible to avoid compacting it, mix well. Divide the mixture into six equal portions and form the portions into patties to fit the buns. When the grill is ready, brush the grill rack with oil. Place burgers on the preheated grill, cover, and cook for 4-5 minutes on one side until well browned, then flip them, baste with the remaining teriyaki sauce, and cook for another 2-3 minutes until almost done (for medium). Add a slice of cheddar cheese to the top of each burger. Cover again and finish cooking the patties and melting the cheese, 1-2 minutes more. Meanwhile, melt the other two tablespoons of butter in a large sauté pan placed on the grill rack. Crack each of the eggs into the pan and cook for about two minutes on one side, then flip each egg and cook for another minute or two on the other side (until the yolk no longer feels runny when you press down on it lightly). Place one fried egg on top of each hamburger patty. While you are frying the eggs, place the egg buns, cut side down, on the outer edges of the rack to toast lightly. For the Japanese-style mayonnaise, mix the mayonnaise with the rice wine vinegar. To assemble the burgers, spread a generous teaspoon of the Japanese-style mayonnaise on the top half of each bun. On each bottom bun, place an equal amount of caramelized onions and one cheese-and-egg-topped hamburger patty. Add the top buns and serve immediately. Makes six burgers.