Mix breadcrumbs and milk in a bowl to moisten. Mince the onion and microwave for 1 minute at 600W, then let cool.

Combine all hamburger patty ingredients in a bowl, mix well, and divide into two portions. Shape into round patties.

Heat 1/2 tbsp salad oil in a pan over medium heat. Cook the patties until browned on one side, flip, cover, and cook on low heat for 7–8 minutes until fully cooked.

Using the same pan, add gravy sauce ingredients and cook until thickened. Remove from heat.

Clean the pan, heat 1 tsp salad oil over medium heat, and fry the eggs sunny-side up. Remove from heat.

Spread mayonnaise on the buns, layer with lettuce, cheese, hamburger patty, and fried egg.