Lay the zucchini, carrot and radish out on a rimmed baking sheet, cover with the onions, sprinkle with the zest and juice and black pepper, and drizzle with olive oil. Let marinate at room temperature for 2 hours.
Crack the eggs into a medium glass bowl, and beat them until they turn pale yellow. Heat a heavy-bottomed nonstick saute pan over medium-low heat; add the butter, and let it melt. Sprinkle the eggs with some salt and white pepper, then grab your whisk and whisk like crazy. When the butter in the pan is hot enough to make a drop of water hiss, pour in the eggs. Let the eggs cook for up to a minute-don't stir!-or until the bottom starts to set.
With a heat-resistant rubber spatula, gently push 1 edge of the eggs into the center of the pan while tilting the pan to allow the still-liquid eggs to flow in underneath. Repeat with the other edges until there's no liquid left. Your eggs should now resemble a bright yellow pancake, which should easily slide around on the nonstick surface. If it sticks at all, loosen it with your spatula.
Gently flip the egg pancake over, using your spatula to ease it over if necessary. Cook for another few seconds, or until there is no uncooked egg left. With your spatula, lift 1 edge of the egg and fold it across and over, so the edges line up; don't overcook or allow the egg to turn brown. If necessary, you can flip the entire omelet over to cook the top for 30 seconds or so. Just don't let it get brown.
Gently transfer the finished omelet to a plate. Serve with the marinated vegetables, and top with pickled vegetables.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.