Preheat the oven to 375°F. Add the flour, salt and pepper to a bowl and mix together. Lightly dredge each piece of chicken in the flour and shake off any excess.
In a large skillet, melt the butter with the olive oil over medium heat.
Add the chicken and sear for 2 to 3 minutes per side, until golden brown. The chicken does not need to be fully cooked. Remove the chicken from the skillet and set aside.
Melt the butter in the same skillet over medium heat. Whisk the flour, salt and pepper and cook for 1 to 2 minutes to remove the raw flour taste.
Add the onion and garlic to the skillet and sauté for 2 to 3 minutes until softened.
Add the sliced mushrooms and dried thyme and cook for an additional 4 to 5 minutes until the mushrooms are tender and any liquid has evaporated.
Gradually whisk in the chicken broth and whipping cream. Cook, stirring constantly, until the sauce thickens, about 3 to 4 minutes. Remove from the heat.
In a 9x13-inch baking dish, arrange the chicken breasts in a single layer.
Pour the mushroom cream sauce over the top. Make sure the chicken is covered.
Lay the slices of cheese over the sauce to cover.
Bake for 25 to 30 minutes or until the chicken is cooked and reaches an internal temperature of 165°F and the cheese is bubbly and golden.
Remove from the oven and let rest for 5 minutes. Garnish with freshly chopped parsley, if using and serve.
Notes
Garnish with freshly chopped parsley if desired. This dish pairs well with steamed vegetables or garlic bread.