Combine dals, rice, and wheat or barley in a medium bowl. Pour in water to cover and swish dals and grains around with your fingers. Drain and repeat the process until water runs clear enough to see your hands through.
Pour in water to cover and let dals and grains soak at room temperature at least 2 hours, or cover and chill up to 12 hours.
Place meat on a plate, pat dry with paper towels, and season all over with 2 tsp. salt; set aside
Finely grate half of ginger; set aside
Thinly slice remaining ginger. Stack slices and cut crosswise into matchsticks; set aside
Combine shallots and ghee in the pot of electric pressure cooker and set to sauté function or high. Cook, stirring often and adjusting heat as needed if your cooker has that option, until shallots are just beginning to brown
Reduce to normal function or medium if possible, or, if your cooker doesn’t have a lower setting, turn off for a minute if mixture is getting too hot
Add reserved ginger matchsticks and cook, stirring often, until shallots are brown and crisp and ginger is frizzled, 4–10 minutes, depending on your cooker
Using a slotted spoon, transfer shallots and ginger to a plate, spreading out into a single layer. Season lightly with salt; let cool
Add garlic, Haleem masala, cayenne, turmeric, and reserved grated ginger, and cook, stirring constantly, until fragrant, about 30 seconds
Add meat and stir to coat in spices. Cook, stirring often with a wooden spoon and repeatedly adding splashes of water as spices begin to stick to bottom of pot and scraping up browned bits, until flavors come together, about 15 minutes
Drain dal mixture and add to pot along with 1 tsp. salt and 5 cups broth
Secure lid and bring to full pressure according to manufacturer’s directions. Cook 1½ hours. Let sit 20 minutes, then manually release pressure and open up
Taste haleem and add more salt and cayenne if needed. Add chiles if using. Simmer on normal function or medium, stirring often, 5 minutes
Stir in ½ cup cilantro
Serve haleem with lime wedges, reserved crispy shallots and ginger, and more chopped cilantro
