Meanwhile, in a large skillet, heat the olive oil and garlic over medium-low heat and cook until the garlic starts sizzling with little bubbles around it. Add the basil and sizzle in the oil until it releases its sweet aroma, about 15 seconds. Add the Arrabbiata sauce, season with a heavy pinch of salt, and cook for about 10 minutes.

Once the water has reached a rolling boil, season with salt until it tastes like a seasoned soup. Working in batches so the gnocchi have plenty of room to move around, drop in the gnocchi and cook just until they float and are tender, 2 to 3 minutes. Transfer the gnocchi to the pan with the sauce, or to a separate baking dish along with the sauce.

Scatter the mozzarella pieces over the gnocchi, then toss gently in the pan until gnocchi, cheese and sauce are mixed. Sprinkle the Parmigiano-Reggiano evenly over the top.

Bake until the mozzarella is melted and a light-brown Parmigiano-Reggiano crust begins to form, 5 to 10 minutes.

Garnish with whole basil leaves and serve immediately.