In a medium saucepan, melt the butter over medium heat; stir in the flour until well combined and cook for 30 seconds, stirring constantly.
Very slowly add in the milk, whisking constantly, until well combined. Cook and stir until bubbly.
Reduce the heat to low and add the cheddar cheese, American cheese, and grated Parmesan cheese; 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 the stove off and let it sit for 3-5 minutes to allow the sauce to thicken. Add a bit of reserved water, if needed.
Stir, taste & re-season, if needed. Spoon into serving bowls, then sprinkle a bit of parsley on top.
Serve immediately, along with extra Parmesan cheese on the side. Enjoy.