Bring a large pot of salted water to a boil. Add the 16-ounce package of potato gnocchi and cook according to package instructions. Before draining, reserve 1 cup of the cooking liquid, then drain the gnocchi.
While the gnocchi cooks (or immediately after draining), heat 2 tablespoons butter in a large skillet over medium heat until melted.
Add the drained gnocchi to the skillet and cook, stirring occasionally, for about 1 minute to warm and lightly brown the gnocchi.
Remove the skillet from the heat. Stir in ½ cup basil pesto, tossing the gnocchi to coat evenly. If the sauce seems too thick, add some of the reserved cooking liquid a little at a time until you reach the desired consistency.
Taste and season with kosher salt as needed.
Divide the pesto gnocchi among shallow bowls, top with freshly grated Parmesan cheese and freshly ground black pepper, and serve immediately.