Toast the sourdough slice in a toaster or on a dry pan until golden and crisp.
In a medium bowl, whisk together the eggs, cottage cheese, sea salt, and black pepper until the mixture is well combined and slightly frothy.
Heat the olive oil in a non-stick skillet over medium-low heat, ensuring the surface is evenly coated.
Pour the egg and cottage cheese mixture into the skillet and let it sit undisturbed for about 30 seconds to begin setting.
Using a silicone spatula, gently push the eggs from the edges toward the center, creating soft curds.
Sprinkle the shredded cheddar cheese over the eggs while they are still slightly wet, folding gently to incorporate as the cheese melts.
Continue to cook slowly until the eggs are just set but still look moist and creamy, then remove from heat immediately.
Pile the cheesy egg scramble onto the toasted sourdough and garnish with chopped fresh chives before serving.