Slice each chicken breast in half horizontally to make 4 thin cutlets, then season both sides with garlic powder and lemon pepper; add salt if your lemon pepper lacks salt.
Heat the olive oil and butter in a large skillet over medium-high heat until hot, then sear the chicken 5–6 minutes per side, until golden and cooked through; transfer to a plate and tent with foil.
Lower heat to medium and add the minced garlic to the same skillet; cook about 30 seconds until fragrant.
Pour in the chicken broth and lemon juice, scraping up any browned bits from the pan.
Stir in the heavy cream and add the uncooked gnocchi, pushing the gnocchi into the liquid so they are submerged; simmer gently, uncovered, stirring occasionally, for 5–7 minutes until gnocchi are cooked and the sauce thickens.
Remove the pan from heat, stir in the grated Parmesan and spinach until the spinach wilts and the sauce is combined.
Return the cooked chicken and any collected juices to the skillet, spoon sauce over the top, season with salt and pepper to taste, and serve immediately.