Rinse the moong dal and rice. (See Note.)
Heat the ghee or coconut oil in a medium-sized saucepan over medium heat. Add the minced ginger, cardamom pods, black mustard seed, cumin seed, fennel seed and fenugreek seed all at once and stir constantly. As soon as the mustard seeds start to pop (after about 1 minute), add the rinsed moong dal and rice, ground cumin, turmeric and coriander. Stir to coat the moong dal and rice with the spices.
Add the bay leaves. Pour in the water and stir. Bring to a boil, turn down to a simmer and cook covered for 30 minutes, remembering to stir every 10 minutes. Turn off the heat once the water is absorbed and the moong dal and rice are cooked. Stir in the salt and, if using, lime juice. Garnish with cilantro before serving, if desired.
Store leftovers in the refrigerator for a week. Reheat portions before serving.