Add olive oil and 1 tablespoon butter to a large skillet on medium high heat.
While the butter melts, season the chicken cutlets with salt and pepper then dredge in the flour and shake off any excess.
Add the cutlets to the pan and cook until golden brown and cooked through to 165°F, about 4 minutes per side. Remove from the pan and tent with foil.
In the same pan melt the remaining tablespoon of butter, then add the mushrooms and thyme. Cook for around 5 minutes, stirring occasionally, until the mushrooms are browned and sizzling. Add the garlic and cook for around 30-45 seconds, stirring constantly to avoid burning.
Add the Marsala wine and chicken broth and simmer for about 5-6 minutes, stirring occasionally. Then stir in the cream and bring to a simmer. Add the chicken back to the pan and cook for an additional 2-3 minutes until the sauce is thickened.
Serve over mashed potatoes, angel hair pasta, mashed cauliflower, or zucchini noodles.
Notes
Cutlets: Slice chicken breasts in half horizontally, or pound them to ¼ to ½ inch thick so they cook evenly.
Marsala: Use dry Marsala, not sweet.
Dairy-free: Leave out the heavy cream for a classic, non-creamy sauce.
Storage: Refrigerate leftovers for up to 4 days. Reheat in a 350°F oven or in a skillet over medium-low heat.