Heat some oil in an iron cast pot. Add the chicken fat and fry for two minutes. Add the chopped onion. When it gets soft and golden, add a pinch of baking soda. The onion will turn yellow, and will get darker gradually. When it get a "yummy" colour, add the chicken parts, garlic cloves, mushrooms and eggplant (if wanted). Mix everything well and keep frying. Meanwhile boil two cups of water or chicken stock.
When the chicken get a good colour, add paprika and the shredded carrot. Let the carrots fry for a minute and than add the rice. Mix everything again. Let the rice to absorb the flavours and than add the boiling water (or the chicken stock). Cover, lower the heat and cook for half an hour or until the rice is done.