In a saucepan, melt the butter over medium heat; stir in the flour until well combined, and cook for 30 seconds, stirring constantly. Slowly whisk in the milk, whisking constantly, until well combined, and cook and stir until bubbly.
Reduce the heat to low and add the cheddar, American cheese, and grated Parmesan; stir until melted. Season with sea salt and freshly cracked pepper, to taste.
Cook the gnocchi in a large pot of salted boiling water, according to the package instructions. Drain, reserving ¼ cup of the cooking water.
Add the cooked & drained gnocchi to the sauce. Toss to coat evenly, then turn off the heat and let it sit for 3-5 minutes to let it thicken. Add a bit of reserved water, if needed.
Stir, taste & re-season, if needed. Spoon into serving bowls, then sprinkle the top with parsley.
Serve immediately, along with extra Parmesan cheese on the side. Enjoy.