Heat the oven. Preheat the oven to 400°F (204°C) and lightly oil a 9x13-inch baking dish or large braiser.
Season the chicken. Pat the thighs dry and season all over with half of the Italian seasoning, salt and pepper.
Sear the chicken. Melt 1 tablespoon of butter in a large skillet over medium-high heat. Sear the thighs skin side down until the skin is deep golden, 5 to 6 minutes, then flip and cook 2 minutes more. Set aside.
Wilt the spinach. Melt 1 tablespoon of butter in the same skillet. Add the spinach and cook, stirring, until it just wilts, about 2 minutes.
Make the sauce. Add the remaining 2 tablespoons of butter and the garlic and cook until fragrant, about 1 minute. Whisk in the broth and remaining Italian seasoning and simmer 1 to 2 minutes. Stir in the cream and Parmesan and simmer until slightly thickened. Season with salt and pepper.
Assemble. Spread the uncooked gnocchi in the baking dish, pour the spinach cream sauce over it and stir to coat. Nestle the chicken thighs in skin side up so the skin sits above the sauce. Sprinkle the mozzarella over the gnocchi, keeping it off the chicken skin.
Bake. Bake for 30 to 35 minutes, until the chicken reaches 165°F (175°F for the most tender thighs), the gnocchi are tender and the cheese is golden.
Rest and serve. Let rest for 5 minutes so the sauce thickens, then garnish with parsley and serve.