Heat ghee in a skillet over medium-low heat. Add onions, cardamoms, cloves, cinnamon stick, bay leaves, and cumin seeds. Cook and stir until onions are lightly browned, about 5 minutes. Add ginger paste and garlic paste and continue to saute for 2 minutes. Add chicken and 1/2 teaspoon salt; cook and stir until chicken is lightly browned, about 5 minutes.
Transfer mixture to a slow cooker. Add chana dal, moong dal, dalia, cayenne pepper, turmeric, and garam masala. Pour water on top and mix to combine.
Cook on Low for 10 to 12 hours, mixing in cilantro and mint 30 minutes before the end of the cook time.
Remove bay leaves and cinnamon stick. Use a hand blender to lightly blend mixture, or skip this step of you like your haleem chunky. Serve hot.