Season chicken slices with salt and pepper, then dredge in flour, shaking off any excess.
Melt 2 tablespoons of butter and 1 tablespoon of olive oil in a large skillet over medium heat.
Add the chicken to the skillet and cook until golden brown and cooked through, about 4-5 minutes per side
Remove the chicken from the skillet and set aside. In the same skillet, add 2 tablespoons of butter and minced garlic. Cook for 1-2 minutes until fragrant.
Pour in chicken broth and heavy cream, stirring constantly until it starts to thicken.
Add the grated parmesan cheese, lemon juice, and lemon zest to the skillet.
Stir until the cheese is melted and the sauce is smooth.
Return the chicken to the skillet and coat with the lemon butter sauce.
Garnish with chopped parsley and serve hot.