Bring a large pot of salted water to a boil and cook 8 ounces spaghetti according to package directions until al dente.
While the pasta cooks, melt 1/2 cup butter in a saucepan over medium heat.
Continue cooking the butter, swirling or stirring occasionally, until it foams and then turns a deep golden-brown and smells nutty, about 4–5 minutes; watch closely so it doesn’t burn.
Drain the pasta in a colander without rinsing, then transfer it to a serving bowl.
Pour the browned butter over the hot pasta, add 1/2 cup grated mizithra cheese, and toss thoroughly to coat.
Finish with chopped parsley if desired and serve immediately.