Ingredients

• 3 tablespoons extra-virgin olive oil
• 1 1/2 pounds onions (2 large), sliced into 1/2-inch-thick rings
• Salt and freshly ground black pepper
• 3 tablespoons seasoned rice vinegar
• 1/2 pound sliced bacon, frozen 1 hour
• 1 1/2 pounds ground beef chuck
• 1 tablespoon Worcestershire sauce
• Salt
• Freshly ground black pepper
• 2 tablespoons unsalted butter, melted
• 4 to 8 thin slices extra-sharp Cheddar
• 4 hamburger buns or alternatives such as kaiser or brioche rolls
• Sliced tomato
• Soft-leaf lettuce leaves or baby arugula
• Special equipment: An instant-read thermometer

Instructions

1. Heat oil in a 12-inch heavy skillet over medium heat until it shimmers, then cook onions with 1/2 teaspoon salt and 1/4 teaspoon freshly ground black pepper, covered, stirring occasionally, until golden and softened, 15 to 20 minutes.
2. Reduce heat to medium-low, then add vinegar, scraping up the brown bits on bottom of the skillet, and cook, uncovered, stirring, until liquid evaporates, 1 to 2 minutes. Season to taste with salt and pepper. Transfer to a small bowl and keep warm, covered.
3. For burgers: Prepare grill for indirect-heat cooking over medium-hot charcoal (medium heat for gas; see grilling procedure ). Meanwhile, cut frozen bacon crosswise into eight sections and distribute evenly in bowl of a food processor, then pulse until finely chopped. In a large bowl, distribute bacon evenly over beef and drizzle mixture with Worcestershire sauce. Sprinkle evenly with 1 teaspoon salt and 1/2 teaspoon freshly ground black pepper. Combine mixture as gently and thoroughly as possible with your fingers (be careful not to overmix). Form into 4 patties, about 4 inches in diameter and 1 inch thick. Brush cut sides of buns with butter. Oil grill rack, then sear patties directly over coals (or lit burner or burners), covered only if using a gas grill, moving to area of grill with no coals (or over shut-off burner) if flare-ups occur, until browned, 2 to 3 minutes on each side. Move burgers to area with no coals (or over shut-off burner) and grill, covered, turning once, until they reach 155°F on instant-read thermometer, about 4 minutes total. Top with cheese to taste and heat, covered, until it melts and burgers register 160°F, about 1 minute. Transfer burgers to a clean platter. Grill buns, buttered side down, until grill marks appear, about 1 minute. Assemble burgers with buns and accompaniments, topping cheese with caramelized onions.
4. Prepare grill for indirect-heat cooking over medium-hot charcoal (medium heat for gas; see grilling procedure ).
5. Meanwhile, cut frozen bacon crosswise into eight sections and distribute evenly in bowl of a food processor, then pulse until finely chopped.
6. In a large bowl, distribute bacon evenly over beef and drizzle mixture with Worcestershire sauce. Sprinkle evenly with 1 teaspoon salt and 1/2 teaspoon freshly ground black pepper.
7. Combine mixture as gently and thoroughly as possible with your fingers (be careful not to overmix). Form into 4 patties, about 4 inches in diameter and 1 inch thick.
8. Brush cut sides of buns with butter.
9. Oil grill rack, then sear patties directly over coals (or lit burner or burners), covered only if using a gas grill, moving to area of grill with no coals (or over shut-off burner) if flare-ups occur, until browned, 2 to 3 minutes on each side.
10. Move burgers to area with no coals (or over shut-off burner) and grill, covered, turning once, until they reach 155°F on instant-read thermometer, about 4 minutes total. Top with cheese to taste and heat, covered, until it melts and burgers register 160°F, about 1 minute. Transfer burgers to a clean platter.
11. Grill buns, buttered side down, until grill marks appear, about 1 minute.
12. Assemble burgers with buns and accompaniments, topping cheese with caramelized onions.