Season the chicken with salt and pepper. Add the flour to a bowl and coat the chicken lightly on all sides.
Heat 2 tablespoons olive oil in a large skillet over medium heat. Cook the chicken until lightly golden on both sides and nearly cooked through. Remove and set aside.
In the same skillet, add 1 tablespoon olive oil and the butter. Add the chopped onion and cook until softened, then stir in the garlic.
Add the mushrooms and cook until softened and lightly golden.
Pour in the stock and simmer briefly, scraping the bottom of the skillet.
Stir in the heavy cream, Parmesan if using, and lemon zest. Season with salt and pepper to taste.
Return the chicken to the skillet and simmer gently until the sauce thickens and the chicken is fully cooked through.
Sprinkle with chopped parsley and serve hot.