Heat olive oil and butter in a large skillet over medium heat.
Season the chicken with salt and pepper, then add it to the pan.
Sear for 5 minutes per side until golden brown. Remove from the pan and set aside.
In the same pan, add the onion and mushrooms (if using).
Cook for 3-4 minutes until softened.
Add the garlic and cook for 30 seconds until fragrant.
Sprinkle flour over the vegetables and stir for 1 minute.
Slowly pour in the white wine, stirring to deglaze the pan.
Add the chicken broth, thyme, and bay leaf.
Return the chicken to the pan, skin side up.
Cover and simmer for 25 minutes, until the chicken is tender.
Stir in the heavy cream and let it cook for 2 more minutes.
Remove the bay leaf and thyme sprig.
Serve hot over mashed potatoes, rice, or noodles.
Garnish with fresh parsley if desired.