Preheat a large skillet to medium heat with the olive oil and 2 tablespoons of the butter. Use a fork to combine the flour in a shallow dish with 1/2 teaspoon pepper and 1 teaspoon salt.
When the skillet is hot, dip each piece of chicken in the flour mixture, shaking off any excess. Place the pieces of chicken in the skillet and let them cook undisturbed for 4 minutes. When the chicken has a light brown crust on the bottom, flip the pieces and cook for 4 additional minutes on the second side or until the chicken is cooked through and both sides are light golden brown.
When the chicken is cooked, remove to a plate or individual plates for serving. Add the mushrooms to the pan immediately and stir to wilt for about 3 minutes. Sprinkle the mushrooms with salt and add the remaining tablespoon of butter.
When the mushrooms are brown and wilted add the cream to the skillet and turn the heat off. Stir gently to warm the cream, and add a few more pinches of salt and pepper to your preference.
Serve the chicken with spoonfuls of creamy mushrooms. Enjoy!