In a nonstick pan, heat butter and scramble eggs gently, do not allow any browning. Using a rubber spatula, shape eggs into four, bun-size portions.
When eggs are cooked, season with salt and pepper and top each portion with a slice of cheese, let stand a minute until cheese starts to melt.
To assemble: Place one-ounce Russian dressing on top of each bun, put one egg portion on the bottom. Then add four pickle slices, one-ounce onion, and one-ounce lettuce on top of each egg. Top with bun.
To ensure food safety, eggs should be cooked until both the yolk and the white are firm. Consuming raw or undercooked eggs may increase your risk of foodborne illness, especially for those with certain medical conditions. For recipes that call for eggs that are raw or undercooked when the dish is served, use either pasteurized shell eggs that have been treated to destroy Salmonella, or use pasteurized egg products.