Preheat the oven to 400 degrees Fahrenheit.
Melt butter in a large cast iron skillet over medium-high heat. Add the chicken drumsticks and brown each side, about 2 to 3 minutes per side. Remove the chicken from the skillet and set aside.
Add the onion and mushrooms to the skillet. Cook for 3 to 4 minutes, until tender. Add the garlic and cook for an additional minute. Careful, do not allow the garlic to burn.
Add the chicken broth, Italian seasoning, salt, and pepper to the mushroom mixture. Return the chicken to the pan. Bake in the preheated oven for 30 to 40 minutes, until cooked through and the juices run clear.
Once the chicken is fully cooked, remove it from the pan. Place the cast iron pan on the stove over medium-high heat. Stir in the cream, parmesan cheese, and mustard. Season with additional salt and pepper, as nessessary. Bring the sauce to a simmer and cook until slightly reduced, about 5 minutes.
Pour the sauce and mushrooms over the chicken and garnish with fresh parsley. Serve immediately.