Whisk the eggs, kosher salt, and black pepper in a large bowl until the mixture looks evenly yellow and lightly foamy. A few bubbles show that air has been worked in, helping the eggs form lighter curds.

Melt the butter in a large nonstick skillet over medium heat, then pour in the egg mixture and sweep the bottom with a spatula as the edges begin to set. Push the set egg toward the center in broad strokes so soft curds gather in large folds.

Scatter in the cream cheese cubes once the eggs are partially set, then fold occasionally until the eggs thicken and begin to hold their shape; taste and serve immediately. Take the skillet off the heat while the curds still look glossy, since their residual heat will finish the last bit of cooking.