Pat the chicken thighs dry with paper towels before seasoning both sides with garlic powder and a generous sprinkling of salt and black pepper. Coat each side of the chicken thighs using ¼ cup of flour.
Heat a large skillet or Dutch oven over medium to medium-high heat. Add the olive oil plus 2 tablespoons of butter to the pan. Once hot and melted, add the chicken, skin-side-down, and let them cook undisturbed for 6-8 minutes. Flip the chicken over and continue to cook on the other side for an additional 6-8 minutes.
Remove the chicken from the pan to a clean plate. In the same pan, melt the remaining butter. Add the shallots and carrots and cook until tender, about 7 minutes, stirring as needed to ensure even cooking.
Add the mushrooms and cook until they release their liquid, reduce, and turn a dark brown.
Combine the sage, thyme, garlic, crushed red chili flakes, and flour with the softened vegetables. Cook, stirring continuously, for about a minute or until the garlic is fragrant.
Increase heat to high and add the chicken broth and white wine, mixing well to combine. Once the cooking liquid starts to thicken, nestle the chicken into the sauce.
Reduce heat to medium-low and allow the chicken to simmer for approximately 20 minutes or until the chicken registers 165 degrees as measured with a digital meat thermometer. (For a thicker sauce, remove the cooked chicken from the pan and allow the sauce to continue to simmer until desired thickness is reached, then return the chicken back to the pan)
Serve with mashed potatoes or crusty bread and garnish with fresh parsley, if desired.