Soak the broken wheat (lapsi) in water for 1-2 hours. Cook in a pressure cooker for about 3-4 whistles. When the consistency is soft and mushy, let it cool and grind into a thick paste.
Wash the minced lamb (kheema) thoroughly by rolling it in water like a ball. Do not separate the kheema to prevent the flavour from getting diluted.Pressure-cook for 2 whistles without adding water because it releases its own water while cooking.
Fry the sliced onions and keep aside for garnishing.
Heat the oil and ghee mixture in a pan. To this, add all the whole spices and keep stirring until they start to change colour. Add the chopped onions and whole green chillies. Fry well till the onions are slightly brown. Add the ginger-garlic paste and cook for a few seconds to get rid of the raw smell of garlic. Add mint and coriander leaves, and cook for a few seconds.
Add the curd, turmeric and red chilly powder. Cook till all the masalas are well-cooked and oil droplets begin to form on the sides of the cooked curd. Add salt after the first boil so that the spices absorb the salt.
Now add the broken wheat (lapsi) and mutton pastes. Keep stirring to prevent it from sticking to the base of the pan. Also, stir from the center to the sides of the pan and press out any lumps to make an even mixture. Keep stirring and cooking the haleem for about 3 boils or approximately 10 minutes to ensure that there are no lumps. Taste and adjust the seasoning.
Before serving, add cream and cook for another 2 mins.
Serve in a plate no deeper than 2-3 inches. Garnish with a generous sprinkle of fried onions, mint leaves, green chilies and wedges of lemon, such that each spoonful has enough garnishing. Squeeze the lemon wedges with a spoon.
Haleem is a meal in itself and does not require any accompaniments.