In a medium mixing bowl, whisk together the large eggs, egg whites, cottage cheese, sea salt, and black pepper until the mixture is well combined and slightly frothy.
Place a large non-stick skillet over medium-low heat and add the grass-fed butter, allowing it to melt and coat the bottom of the pan.
Pour the egg mixture into the skillet and let it sit undisturbed for about 30 seconds until the edges begin to set.
Using a silicone spatula, gently push the eggs from the outer edges toward the center, creating large, soft curds.
Continue to cook slowly, folding the eggs over themselves until they are mostly set but still appear slightly moist.
Sprinkle the shredded sharp cheddar cheese over the eggs and fold gently for another 30 seconds until the cheese is melted and incorporated.
Remove the skillet from the heat immediately to prevent overcooking, and garnish with the freshly chopped chives.
Toast the sourdough bread and serve it alongside the warm, cheesy scrambled eggs.