Slice each chicken breast horizontally to create 4 thin chicken cutlets.
Season both sides with salt and black pepper.
Sprinkle flour over the chicken and lightly coat all sides.
Melt 1 tablespoon butter in a large skillet over medium-high heat.
Add the chicken and cook for about 2 1/2 minutes per side until golden brown and fully cooked.
Transfer chicken to a plate and keep warm.
In the same skillet, melt the remaining butter over high heat.
Add mushrooms and cook for 4 minutes until golden around the edges.
Stir in minced garlic and cook for 1 more minute.
Add the chicken stock and scrape the bottom of the pan to release flavor.
Pour in the remaining stock and simmer for 1 minute.
Add heavy cream and reduce heat to medium.
Simmer for 2 minutes until the sauce thickens slightly.
Stir in parmesan cheese until melted and smooth.
Return the chicken to the skillet and spoon the creamy mushroom sauce over the top.
Garnish with chives and serve immediately.