Heat 1 tsp of butter in a frying pan. Put 10 to 12 onion rings, 10 to 12 thin slices of green capsicum, and 10 to 12 thin slices of fresh carrot in it. Stir and fry them for 2 to 3 minutes on a medium flame until the onions turn translucent and others soft.
Now, add a pinch of black pepper powder and regular table salt to taste. Mix them nicely. Keep them aside when done.
Take a burger bun. Cut it into two halves horizontally.
Now, heat 1 tsp of butter in the same frying pan. Put the burger inside down as shown. Remove when golden brown.
Apply 1 tbsp of mayonnaise on the inside of the base part of the bun.
Make a bed of the vegetables.
Put 2 circular pieces of fresh tomato.
Put a cheese slice on top.
Put ½ tsp of butter in a frying pan. Crack one egg. Add a pinch of salt.
Take a round hollow lid of a container to make a round shape. Remove the extra egg white with the spatula.
Put the egg poach gently on top of the cheese slice.
Put a few onion rings, a few shredded pieces of fresh cabbage, and 1 tsp of tomato sauce on it.
Put some more fried vegetables and a few large pieces of cabbage leaves on top.
Apply 1 tbsp of mayonnaise on the top part of the bun. Put it on top. Repeat the steps to make another.
Your homemade egg burgers are ready. Serve them on a plate and enjoy.