Preheat oven to 425 degrees F. Spray an 8x8’’ baking dish with non-stick cooking spray and set aside.
Prepare Glaze: Melt butter in a small saucepan over medium heat. Add shallots and season with 1/4 teaspoon salt. Sauté until soft and translucent, about 3-4 minutes. Add in garlic and sauté until fragrant, 30 seconds- 1 minute. Add in fig preserves, honey, balsamic vinegar and sprig of thyme. Increase heat to bring mixture to a boil and immediately reduce heat to maintain a simmer. Simmer, stirring occasionally, until thickened and reduced by half, about 10-12 minutes. Use tongs to remove thyme sprig and discard.Optional for smoother glaze: Use an immersion blender (or transfer glaze to a stand blender) and puree until smooth.
Meanwhile, season chicken: Place chicken on a clean work surface and pat the chicken dry. Season both sides of the chicken generously with salt and pepper. Transfer chicken to the prepared baking dish (they should fit snugly). Spoon the reduced glaze over the chicken, using the back of a spoon to evenly coat and distribute the glaze. Add 4 remaining sprigs of thyme to the pan.
Roast: Transfer the baking dish to the oven. Bake (basting the chicken with the glaze once during cooking), for 35-40 minutes or until the juices run clear and chicken is cooked through (internal temperature of 165 degrees F. Remove from oven and let chicken rest 5 minutes. Optional: Switch oven to broil during last 3-4 minutes of baking for a more golden brown chicken. Watch the chicken carefully as it can burn easily!!
Serve: Garnish chicken with fresh thyme, walnuts and cheese if using. Enjoy!
Store leftover Balsamic Fig Chicken in an airtight container in the refrigerator for up to 4 days.