Cut long slits into the brinjal by keeping the head and the bottom intact. Check if there are any insects inside the brinjal or not. Then keep the brinjal or eggplant over a wire rack on an open flame to roast it.
Using a tong, turn it around to roast it evenly on all sides. So, once it is completely soft with charred skin, turn off the heat and let the brinjal cool down.
While it is cooling down, finely chop onions and garlic cloves. Julienne the ginger, chop the green chillies and the coriander leaves.
Peel off the skin of the brinjal and discard. Then cut the head and with a masher or a fork, mash the roasted brinjal/eggplant.
Break one egg in a bowl and whisk it and keep aside.
In a kadai, heat mustard oil and add chopped garlic. Let it get a light golden colour. Add the onions and keep frying on medium to high heat.
Once the onions have softened and have started turning golden, add the chopped tomatoes.
Sprinkle salt and turmeric powder and keep stirring. Then add chopped green chillies (if you have a high tolerance for spice) now or else you can add green chillies in the end. Also, add only half of the ginger now to cook with the tomatoes.
In case anything is sticking to the bottom of the kadai, sprinkle some warm water and keep stirring.
Once the tomatoes have softened, add the mashed eggplant. Mix everything thoroughly and stir for a couple of minutes.
Make a well in the centre of the kadai, and add the whisked egg.
Reduce the heat to a minimum and scramble the egg with the brinjal, while stirring continuously. It takes 4 to 5 minutes for the egg to completely cook with the brinjal. It becomes creamy with the roasted eggplant.
Season if required. Sprinkle coriander leaves, green chilies and the balance ginger julienne and turn off the heat.
Serve beguner khagina with steaming hot rotis or rice or even paratha.