In a large skillet, melt butter on medium-high heat. Add onions and sauté until they are clear and translucent. Add garlic and mushrooms, cooking until tender and fragrant. Reserve to the side.
Using the same pan, add oil and cook chicken over medium-high heat. Turn each piece after about 3 minutes.
Turn down heat and return cooked vegetables to pan. Add thyme, rosemary, mustard, cream, Parmesan cheese, salt, and pepper.
Simmer for about 10 minutes, until the sauce is a bit thick and creamy, then serve.