Heat oil in a large and wide pan. Make eggs sunny side up style and sprinkle finely sliced small onion, 1 finely chopped green chilli and chopped curry leaves on top of the eggs. season with salt and pepper. Cook till the eggs are done, transfer to a plate.
Heat more oil in the same pan and add chopped onions. Cook till it browns.
Add crushed ginger & garlic and green chilli (2 slit lengthwise). Cook for 2-3 mins, till the raw smell goes.
Add turmeric, coriander and pepper powders. Mix well. Cook for 2 mins and add 1 tbsp hot water.
Add diced tomato and cook till it becomes soft. Add 2 tbsp hot water to bring the masala together.
Add thick coconut milk and cook till the bubbles form around the edges.
Reduce flame to lowest and cook for 5 mins. . Remove from fire and add cooked eggs.
Notes
You can make the gravy in advance and store it in the refrigerator. It's better to do the egg preparation, just before serving. You can cook the egg according to your taste preferences - easy, over easy, medium done...