01 -
Heat 1 tablespoon oil in a broiler-safe skillet over medium-high heat. Season chicken with 1/4 teaspoon each salt and pepper. Cook, flipping once, until golden and internal temperature reaches 165°F, about 6 minutes. Transfer to a plate.
02 -
Reduce heat to medium. Add 2 teaspoons oil and broccoli to the skillet. Cook, stirring occasionally, until browned, about 5 minutes. Add water, cover, and cook until tender, about 5 minutes more. Transfer broccoli to the plate with the chicken.
03 -
Add remaining 1 teaspoon oil, onion, and mushroom to the skillet. Cook, stirring occasionally, until lightly browned, 5 to 8 minutes.
04 -
Stir in balsamic vinegar, Worcestershire sauce, Dijon mustard, thyme, remaining salt and pepper, and any chicken juices. Cook for 1 minute, scraping up browned bits.
05 -
Preheat broiler to high with rack in upper third of oven. Return chicken to skillet and top with mushroom mixture. Arrange broccoli around chicken. Top with cheese. Broil until cheese is golden, 1 to 2 minutes.
06 -
Garnish with parsley and additional thyme if desired. Serve immediately.