Step 1

Arrange a rack 6 to 8 inches below the broiler element and heat the oven to 400°F. Meanwhile, bring a large pot of heavily salted water to a boil. Grate 3 ounces Parmesan cheese on the smaller holes of a box grater into fine shreds (about 1 1/2 cups), or measure out 3/4 cup store-bought grated. Grate 2 garlic cloves on the same holes of the box grater, or mince. Finely chop 4 fresh chives if desired.

Step 2

Add 2 (about 16-ounce) packages gnocchi to the boiling water and stir to separate the gnocchi. Cook until just tender, 2 to 3 minutes or according to package instructions. Drain the gnocchi.

Step 3

Melt 3 tablespoons unsalted butter in a 10-inch broiler-proof high-sided skillet or 12-inch cast iron skillet over medium heat. Add the garlic and cook until fragrant, about 1 minute. Sprinkle in 3 tablespoons all-purpose flour and whisk for 1 minute to cook the floury taste out. While whisking constantly, slowly pour in 3 cups whole or 2% milk and continue whisking, scraping along the edges of the skillet with a flexible spatula occasionally, until smooth. Stir constantly until the sauce comes to a simmer.

Step 4

Remove the pan from the heat. Add 1 1/4 teaspoons kosher salt and two-thirds of the Parmesan (1 cup freshly grated or 1/2 cup store-bought grated), and stir until melted and smooth. Add the gnocchi and stir gently until the gnocchi is evenly coated with sauce. Taste and season with kosher salt as needed. Sprinkle evenly with the remaining Parmesan (1/2 cup freshly grated or 1/4 cup store-bought grated).

Step 5

Transfer the skillet to the oven and bake until the sauce is bubbling around the edges, 7 to 12 minutes. Turn on the broiler to high and broil until the top is golden-brown in spots, 2 to 7 minutes. Let cool for 3 minutes. Top with a few grinds of freshly ground black pepper and the chives if desired before serving.