Begin by placing the chicken breasts between two sheets of plastic wrap. Use a meat mallet to gently pound the chicken to an even thickness, about ½ inch.
Season the chicken breasts generously with salt and pepper on both sides.
In a large skillet, heat 2 tablespoons of olive oil over medium heat. Once hot, add the chicken breasts in a single layer. Cook for about 4-5 minutes on each side until golden brown and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add 2 tablespoons of butter. Once melted, add the sliced mushrooms and sauté for about 5 minutes until golden and tender. Stir in the minced garlic and Italian seasoning, cooking for an additional minute.
Pour in the chicken broth and bring to a simmer, scraping up any browned bits. Cook for about 3-4 minutes until slightly reduced. Stir in the heavy cream and simmer for another 5 minutes.
Return the chicken to the skillet, spooning the creamy mushroom sauce over each piece. Cook for an additional 2-3 minutes to heat through. Adjust seasoning if necessary.
Garnish with fresh chopped parsley and serve immediately over pasta, rice, or with steamed vegetables.