Melt the butter in a large skillet. Add Gnocchi and cook on high heat, stirring frequently for about 4 minutes. Continuously spread Gnocchi evenly in the pan for crisp texture on both sides.
At the same time, heat the oil in another large skillet over medium-high heat. Add the garlic and cook until fragrant and golden, 1-2 minutes. Add the tomatoes and cook, stirring, until the tomatoes wilt and begin to release their water, 3-4 minutes. Add the baby spinach, season with salt and pepper, stir and add the gnocchi.
Toss to combine and cook for 1 more minute on high heat. Season with more salt and pepper to taste. Divide among plates, garnish with Parmigiano Reggiano shavings and serve.