Pat chicken dry with paper towels and season both sides generously with salt and pepper. Heat butter in a large cast iron skillet over medium-high heat until foaming, then add chicken pieces skin-side down and sear for 4-5 minutes until golden brown before flipping to cook the other side for 3 minutes.

Remove chicken to a clean plate and set aside temporarily. Add diced onion to the same skillet and sauté for 2-3 minutes until softened, then stir in minced garlic and cook for 30 seconds until fragrant and aromatic.

Pour in chicken broth, maple syrup, apple cider vinegar, and Dijon mustard, stirring to combine and scraping any browned bits from the bottom of the pan. Add dried thyme and return the chicken to the skillet, nestling pieces among the liquid.

Add sliced apples and Brussels sprout halves around the chicken, then reduce heat to medium and cover with a lid for 15-18 minutes until the chicken reaches 165°F internally and vegetables are tender-crisp. This cozy fall skillet chicken maple glazed should have the Brussels sprouts just beginning to brown at their edges.

While the skillet braises, whisk cornstarch and water together in a small bowl until smooth and lump-free. Uncover the skillet and drizzle the cornstarch slurry over everything while stirring gently to coat, then simmer uncovered for 2-3 minutes until the sauce thickens into a glossy, coat-the-back-of-a-spoon consistency.

Taste the maple chicken and adjust seasonings with additional salt, pepper, or apple cider vinegar as needed. Transfer to a serving platter and garnish with fresh thyme sprigs if desired before serving immediately.