In a 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 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 salted boiling water, per package instructions. Drain, reserving 1/4 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 with extra Parmesan cheese on the side. Enjoy.