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Put the butter in a medium skillet over medium-low heat.
Break the eggs into a medium bowl, add the Parmesan and half-and-half, and season with salt and pepper. Beat vigorously for about 1 minute.
When the butter melts, add the egg mixture to the skillet.
Cook for about 20 seconds, then stir gently.
Continue to cook, stirring every 15 to 20 seconds, until the eggs are mostly thick and pale yellow but not fully cooked, about 3 minutes.
Remove from the heat, still stirring gently; the eggs will continue to cook from the heat of the pan.
Serve immediately.