Trim thick asparagus with a peeler, leaving them ½-inch thick, or snap off or cut the rough ends.
Melt the butter in a large skillet over medium heat. Add the asparagus and season with salt and pepper. Cook, stirring often, until the asparagus is just tender, 5 to 6 minutes, lowering the heat if needed to keep the asparagus from browning. Don't overcook, the asparagus will soften a little more as it cools. Remove the pan from heat. Sprinkle in parsley and 3 tablespoons of the cheese.
Transfer to a serving dish, and top with the remaining cheese. Serve immediately.