Season the chicken breasts generously with salt and pepper. In a large skillet, heat olive oil and butter over medium-high heat. Cook the chicken for 6-7 minutes on each side until golden brown and the internal temperature reaches 165°F. Remove from skillet and let rest for 5 minutes before slicing.

Bring a large pot of salted water to boil. Add potato gnocchi and cook for 2-3 minutes until they float. Remove with a slotted spoon and set aside, reserving some pasta water.

In the same skillet, add more olive oil if necessary and sauté minced garlic until fragrant. Stir in lemon zest, juice, and chicken broth, and bring to a simmer. Cook for 2-3 minutes to meld flavors before adding heavy cream.

Pour in heavy cream and stir. Simmer for another 3-4 minutes until sauce thickens. Adjust seasoning with salt and pepper.

Add the gnocchi and sliced chicken back into the skillet with lemon sauce. Stir gently to coat and heat through for about 2 minutes.

Remove from heat and garnish with parsley and optionally Parmesan cheese. Serve hot with crushed red pepper flakes if desired.