Finely snip the chives into 1/8-inch pieces and set aside. Crack the eggs into a bowl and whisk them together with the salt and black pepper until well combined and no streaks of white remain. Place a non-stick skillet over medium heat and add the butter, allowing it to melt completely and foam slightly, about 1 minute. The foaming indicates the butter is hot enough to cook the eggs gently without browning.
Pour the whisked egg mixture into the foaming butter and let it sit undisturbed for about 30 seconds to allow the bottom to set slightly. Then gently push the eggs from the edges toward the center with a spatula, tilting the pan so uncooked egg flows to the hot surface. Continue this gentle folding motion for 1-2 minutes until the eggs begin to form soft curds but are still quite wet—they should look undercooked at this point since they'll continue cooking when you add the cottage cheese.
Add the cottage cheese directly to the partially cooked eggs and gently fold it in, distributing it evenly throughout. I like to use a gentle hand here since cottage cheese can break apart if overmixed, and those soft curds are part of the appeal. Continue stirring and folding gently for 3-4 minutes over medium heat until the eggs are cooked through but still creamy and tender, not dry or rubbery. The residual heat will finish cooking the eggs while the cottage cheese adds richness and keeps everything moist.
Remove the skillet from heat and fold in the snipped chives, reserving a small pinch for garnish if desired. Divide the scrambled eggs between plates immediately while they're still warm and creamy.