Make the brown butter by heating the butter in a large skillet over medium heat, stirring constantly, until melted. It will start to bubble, foam, separate, and turn golden brown with a nutty aroma. Side Note: Watch it carefully while cooking because it can burn quickly & easily.
Add the broccoli and a dash of crushed red pepper flakes, then toss to coat evenly in the brown butter.
Cover with a lid and cook for 2 minutes. Remove lid and stir, then cover and steam for 1-2 minutes, or until the broccoli is crisp-tender. Season with sea salt and freshly cracked pepper, to taste.
Pour the broccoli into a serving dish, sprinkle with mizithra cheese, and serve additional cheese on the side.