Spiralize or shred zucchini into noodle-like strands.
Spread zucchini over paper towels, lightly salt and let sit for 10-15 minutes.
Melt butter over medium heat, stirring frequently while swirling pan. Once it begins to bubble, watch for color changes: yellow to tan, and finally a golden brown. Remove from heat and transfer to a bowl once the golden brown color is reached.
Blot excess moisture out of zucchini noodles.
Coat a saute pan with a tablespoon of the browned butter. Saute the zucchini noodles over medium heat for 3-5 minutes.
Drizzle remaining browned butter over zucchini noodles and sprinkle Mizithra cheese on top. Toss to evenly coat and serve immediately.