Dredge the thinly pounded chicken medallions in a mixture of flour, parmesan, salt, and pepper. Shake off excess.
Heat olive oil and butter in a large skillet over medium-high heat. Sear chicken until golden and cooked through, then set aside.
In the same pan, sauté shallots and garlic until fragrant. Pour in chicken stock, lemon juice, and zest, scraping up any browned bits.
Stir in heavy cream, capers, and remaining butter for a smooth, rich sauce.
Cook the gnocchi separately as per package instructions, then toss it into the sauce.
Return the chicken to the pan, spooning sauce over it. Simmer briefly to meld flavors.
Garnish with fresh basil and extra parmesan before serving.
Serve hot and enjoy with a side of Caesar Salad or Focaccia.