Bring a large pot of salted water to a boil and cook the pasta according to package directions until al dente; drain in a colander but do not rinse.
While the pasta cooks, melt the butter in a saucepan over medium heat.
As the butter melts, skim off any foam with a spoon, then continue cooking until the butter turns golden brown and gives a nutty aroma, watching closely to avoid burning.
Place the drained pasta in a large mixing bowl, pour the browned butter over it, then add the grated Mizithra and Romano cheeses.
Toss vigorously until the pasta is evenly coated with butter and cheese; taste and adjust seasoning if needed.
Sprinkle with the minced parsley and serve immediately.