Preheat your oven to 400°F (200°C) and lightly grease a baking dish.

Sprinkle salt and pepper over the chicken breasts and coat them lightly with flour. Shake off any excess flour.

In a large skillet, melt 2 tablespoons of butter and olive oil over medium-high heat. Add the chicken breasts and cook them until they are golden brown on both sides. Transfer the chicken to the prepared baking dish.

In the same skillet, melt the remaining 2 tablespoons of butter and add the sliced mushrooms. Sauté the mushrooms until they are tender and golden brown.

Add the minced garlic and cook for an additional minute until fragrant.

Pour the dry Riesling wine into the skillet and scrape up any browned bits from the bottom. Let it simmer for a few minutes to reduce slightly.

Add the heavy cream, chicken broth, fresh thyme leaves, salt, and pepper to the skillet. Stir everything together and bring the mixture to a simmer.

Pour the sauce over the chicken in the baking dish.

Bake the chicken in the preheated oven for 25-30 minutes or until the chicken is cooked through and the sauce is bubbling.

Garnish with freshly chopped parsley and serve hot, accompanied by your choice of sides.