In a medium bowl, crack the eggs.
Whisk gently until the yolks and whites are just combined—be careful not to overbeat.
Stir in the heavy cream and season generously with salt and pepper.
Place a medium nonstick skillet over medium heat for about a minute to warm up.
Add the butter and swirl to coat the pan as it melts. Just as the melting is complete, before it begins to foam, reduce the heat to low.
Pour the egg mixture into the skillet.
Let it sit for a moment, then begin stirring slowly and occasionally with a wooden spoon or silicone spatula. The key here is low heat and patience.
Continue to cook, stirring and scraping the bottom of the pan, for 10-30 minutes. The eggs will slowly transform from liquid to soft, small curds.
Keep stirring until they reach a creamy, custardy consistency.
Serve immediately for the best texture.
Remove the eggs from the heat just before they look fully cooked. The residual heat in the pan will continue to cook them to the perfect soft, creamy consistency.