In a cast iron skillet or another heavy bottom pan, heat ghee. Once the ghee is medium hot, add jeera seeds and saute till golden brown
Add the onions and chopped green chillies and fry till the onions turn translucent.
Add ginger-garlic paste and tomatoes and fry further till tomatoes are cooked. This will take about 4-5 minutes.
Whisk the 6 eggs together in a large bowl and add to the cooked tomatoes.
Cook on low flame till the eggs are cook. Its important to cook on low flame for light and fluffy textured bhurji.
When the eggs are 80% add, stir in the coconut milk if using. This makes the bhurji a little more creamier.
Once cooked, garnish with coriander leaves and serve hot,