Preheat oven to 450°F with a rack in the center. Halve and thinly slice 1 yellow onion. Cut ½ lb broccoli into 1-inch florets, if necessary. Finely chop 1 teaspoon of garlic.

Heat 1 tablespoon butter and 1 tablespoon olive oil in a medium skillet over medium-high. Add onions and cook, stirring, until very soft, 3-4 minutes. Season with a pinch each of kosher salt and ground pepper. Stir in chopped garlic and ¼ cup water. Cook, stirring occasionally, until liquid is reduced by half and onions are well browned and jammy, 1-2 minutes more. Stir in ½ teaspoon balsamic vinegar (or red wine vinegar).

While onions cook, cut 2 pieces of aluminum foil into 12x20-inch rectangles. Pat 10 oz boneless, skinless chicken breast dry and season all over with kosher salt and ground pepper.

Place chicken and broccoli next to each other in center of each foil piece. Drizzle broccoli with olive oil and season with salt and pepper. Spread caramelized onions over chicken, then sprinkle with 2 oz shredded fontina. Fold sides of foil over top and pinch edges to seal (leave room inside packets for air to circulate). Transfer to a rimmed baking sheet.

Roast packets on center oven rack until chicken is cooked through, about 15-20 minutes. Remove from oven and switch oven to broil. Carefully unwrap top of foil to expose chicken and broccoli. Broil French onion chicken and broccoli on center oven rack until cheese is browned, about 2-3 minutes (watch closely as broilers vary). Enjoy!