Place nonstick skillet over medium-low heat. Add white truffle oil and let it heat up a little. In a medium bowl, add eggs, half and half, and a little salt and pepper. Whisk until combined. Add to nonstick skillet and leave undisturbed. Place sour dough slices in the toaster.
Once the edge of the eggs starts to cook slightly, gently fold eggs over each other to cook the eggs more and prevent them from browning. Add chopped chives. Remove from heat right before the eggs finish cooking.
Butter the toasted slices of sourdough. Split eggs over the two slices. Sprinkle with chives for garnish and a pinch more of pepper. Serve immediately.