Start by seasoning the chicken cutlets with salt and pepper. Then sprinkle flour over each cutlet and spread to cover.
In a large skillet, melt butter over medium heat, swirling the pan to coat with melted butter.
Add chicken to the pan, working in batches if needed to avoid crowding the pan. Cook for 4-5 minutes on each side, or until golden brown and cooked through to a temperature of 165°F/74°C. Transfer chicken to a plate, cover to keep warm, and set aside.
Add remaining butter to the pan, add the sliced mushrooms, season with salt and pepper and saute until the mushrooms start to soften and have a golden brown edge.
Add the garlic and cook briefly for about 30 seconds, while stirring.
Deglaze the pan with chicken stock, scraping up any bits that have stuck to the bottom of the pan. Bring to a boil then reduce the heat and let it simmer until it’s reduced and thickened.
Add the cream, whisk everything together to warm through. Add parmesan. Taste the sauce and add additional salt if needed.
Return the chicken to the skillet, spoon the sauce over the chicken. Garnish with fresh herbs before serving (parsley, basil, or chives).