In a large pot, bring salted water to a boil. Add the potato gnocchi and cook according to package instructions until they float to the top. Drain and set aside.
In a large skillet, heat the olive oil over medium heat. Add the minced garlic and sauté for about 1 minute until fragrant.
Pour in the chicken broth and heavy cream, stirring to combine. Bring the mixture to a gentle simmer.
Add the shredded chicken, lemon zest, and lemon juice to the skillet. Stir well and let it simmer for about 5 minutes.
Add the cooked gnocchi and chopped spinach to the skillet. Stir gently until the spinach wilts and everything is heated through, about 3-4 minutes.
Season with salt and pepper to taste. Stir in the grated Parmesan cheese until melted and creamy.
Serve immediately, garnished with fresh parsley.