Preheat the oven to 400F/200 C. Chop the onions, slice the carrot and mushrooms, and mince the garlic. Season the chicken with ½ tsp salt and ¼ tsp black pepper.
Place a heavy skillet over high heat and add the oil. Add the chicken drumsticks. Brown for 7 minutes, flip and brown the other side for 5 more minutes. Transfer to a plate.
Add the butter to the skillet. Add the onions, carrots, and mushrooms. Cook for 5-7 minutes, or until the mushrooms are golden.
Add the garlic and cook for 1 minute or until fragrant. Add the wine, chicken broth, and pearl onions and stir. Scrape off all the bits from the bottom of the pan.
Return the chicken to the skillet (skin side up for the thighs). Bake for 20-25 minutes or until the chicken is cooked all the way through. Take the skillet out of the oven and place it over medium heat.
Transfer the chicken to a plate. Mix in the heavy cream and xanthan gum, mix and simmer the sauce for 5 minutes. Add the lemon juice and parsley, and stir.
Taste the sauce and season if needed. Return the chicken to the pan and garnish with more chopped parsley. Serve immediately!