Step 1: In a shallow bowl, whisk together the flour, salt, and pepper. Dredge each chicken breast in the flour mixture, shaking off any excess.
Step 2: In a large skillet over medium-high heat, melt 2 tablespoons of butter with the olive oil. Add the chicken in batches and sear until golden brown, about 3-5 minutes per side. Remove chicken from the pan and set aside.
Step 3: In the same skillet, add the remaining butter and the sliced mushrooms. Sauté until the mushrooms are browned and tender, about 5-7 minutes.
Step 4: Add the shallots and garlic to the pan and cook for another 1-2 minutes until fragrant.
Step 5: Pour in the Marsala wine and chicken stock, using a wooden spoon to scrape the browned bits from the bottom of the pan. Bring to a simmer and let the liquid reduce by half.
Step 6: Stir in the heavy cream and return the chicken to the skillet. Simmer for 2-3 minutes until the sauce thickens and the chicken is heated through.
Step 7: Garnish with fresh parsley and serve immediately over your choice of pasta or potatoes.