1. Season chicken with salt and pepper. In a large skillet over medium heat, heat oil. Cook chicken until golden, about 2 minutes per side. Remove from pan and keep warm on a plate.
2. To same skillet over medium heat, melt butter. Add shallots and mushrooms and cook until soft, 5 minutes. Add garlic and cook until fragrant, 1 minute more. Season with salt and pepper.
3. Add wine and broth and scrape up any bits off bottom of pan. Bring to a simmer and let simmer until reduced by at least half, it should have thickened. Add crème fraîche, rosemary, and thyme and return to a simmer.
4. Return chicken to skillet and spoon sauce over. Continue to simmer until heated through, 5 minutes.
5. Garnish with parsley before serving.