In a bowl, whisk together the eggs, heavy cream, and salt until the mixture is very smooth and airy. For extra silky eggs, you can strain the mixture through a fine mesh sieve.
Heat a nonstick or stainless steel pan over medium-low heat and melt the butter to coat the surface.
Pour in the eggs and let them sit for a few seconds until the edges just begin to set.
Using a spatula or wooden spoon, gently stir in a circular motion to fold the eggs into soft spirals as they cook.
Continue folding until the eggs are just set but still glossy and tender, then remove from the heat right away to prevent overcooking.
Garnish with finely chopped chives, more salt to taste, and a crack of black pepper before serving.