Cheddar Burgers with Balsamic Onions and Chipotle Ketchup
Beef
1 pound red onions, cut crosswise into 1/3- to 1/2-inch-thick rounds
Olive oil
¾ teaspoon coarse kosher salt
½ teaspoon coarsely ground black pepper
2 tablespoons balsamic vinegar
1 cup ketchup
1½ teaspoons chopped chipotle chiles from canned chipotles in adobo, plus 2 tablespoons adobo sauce
2 teaspoons (or more) balsamic vinegar
2¼ pounds ground beef (15 to 20% fat)
Coarse kosher salt
6 thick slices sharp cheddar cheese
6 hamburger buns, split, cut sides grilled
6 tomato slices (optional) 2 cups fresh spinach leaves
Prepare barbecue (medium-high heat). Arrange onion rounds on baking sheet. Brush with oil; sprinkle with ¾ teaspoon kosher salt and pepper. Transfer onion rounds (still intact) to grill rack; close cover. Cook until grill marks appear, about 4 minutes per side. Reduce heat or move onions to cooler part of grill. Close cover; cook until onions are tender, about 10 minutes. Transfer to medium bowl. Toss with vinegar. (Do ahead: can be made 3 days ahead. Cover; chill.)
Mix ketchup, chiles, adobo sauce, and 2 teaspoons vinegar in small bowl. Season with salt and more vinegar, if desired. (Do ahead: can be make 3 days ahead. Cover and chill.)
Shape beef into six 1/2-inch thick patties. Sprinkle patties on both sides with coarse salt and pepper. Prepare barbecue (medium-high heat). Place burgers on grill. Close cover; cook burgers until bottoms start to darken and juices rise to the surface, about 3 minutes. Turn burgers; cook to desired doneness, about 3 minutes longer for medium-rare. Top with onions and cheese. Close cover; cook until cheese melts. Place bun bottoms on plates; spread with ketchup. Top with burgers, tomatoes (if desired), spinach, and bun tops. Serve, passing remaining ketchup separately.