Heat the skillet on medium-high heat.Once hot, add 1 tablespoon of oil then chicken. Salt and pepper the chicken. Cook until the chicken is cooked through with no pink. Transfer to a clean plate. Set aside.
To the skillet, add the gnocchi, broccoli, and chicken broth. Cook until the gnocchi is soft and broccoli is cooked to tender/crisp. Add the chicken back into the pan. Add garlic and cook until fragrant.Pour in half and half, parmesan, salt, and pepper to taste, stir to coat. Cook a couple of minutes to allow the sauce to thicken. Serve immediately.
Store in an airtight container in the refrigerator for up to 4 days.