1. Heat butter in large nonstick skillet over medium heat until hot. Crack eggs into pan one at a time. Break the yolks and gently whisk the eggs. Allow the eggs to set, then with a spatula gently scrap the eggs across the pan forming large soft curds. Let sit again until eggs set, then scrape again, repeating until thickened and no visible liquid egg remains.
2. Transfer eggs to plate, sprinkle with fresh dill, and season with salt and pepper. Serve with tomato and cucumber.