Cut each chicken breast in half horizontally. Pound the chicken breasts lightly with a meat mallet until about ½ inch thick.

Season the breasts with kosher salt and freshly ground black pepper then melt the butter in a large skillet with half of the olive oil. Add 2 of the chicken breasts to the skillet and cook for 5-7 minutes on each side. Transfer the chicken breasts to a plate.

Add 1 tablespoon of butter and the rest of the olive oil to the pan then repeat with the remaining chicken breasts. Cook and transfer to the plate with the other breasts, then cover to keep warm.

Add 1 more tablespoon of the butter to the skillet and melt over medium heat. Add the mushrooms and shallots to the skillet and cook for 4-5 minutes until softened, stirring often.

Add the wine and chicken broth to the skillet, bring to a boil, and reduce to half. Add the whipping cream, thyme leaves and the last tablespoon of butter. Stir to combine and add the lemon zest.

Serve the mushroom sauce over the chicken breasts. Garnish with chopped parsley, more fresh thyme leaves and additional lemon zest if desired.