Heat a large skillet over medium heat and add the olive oil. Add the onions and a pinch of salt. Stir to coat and cook, stirring periodically, for 10 minutes, until just translucent. Turn the heat down to medium low or low and continue cooking the onions, stirring every once in a while. You should hear a gentle sizzle coming from the onions at all times, so adjust the heat accordingly. Cook until the onions are golden brown, soft, and jammy, which takes anywhere from 40 minutes to 1 hour or more, depending on the onions.
Crack the eggs into a medium bowl and add ⅛ teaspoon of salt. Use a whisk to vigorously whip the eggs until completely smooth and streak free. Heat a medium non-stick skillet over medium-low heat. Add the butter and swirl it around until completely melted. Add the eggs and do not stir, until you see them just starting to set at the edges. Use a spatula to push the eggs from the edges and across the skillet in quick, confident motions. Continue to move the eggs around and cook for about 2 minutes total, until the eggs are fluffy and mostly set, but still glossy and runny on top. The eggs will continue cooking once you remove them from the heat. Serve right away, topped with the caramelized onions, black pepper, and herbs, if using.
Soft scrambling eggs is one of the most decadent, yet simple egg preparations, which yields an incredibly custardy and lush scramble. A topping of slow-caramelized onions takes the decadence factor to the next level.