Chill meat in the freezer until firm but not frozen, 2 1⁄2–3 hours, then pulse in a food processor until a semismooth paste forms. Transfer to a medium bowl and set aside. Put papaya and 1⁄4 cup cold water into a blender and purée until smooth. Add papaya paste and salt to meat and mix well. Cover and let marinate at room temperature for 1 hour.
Meanwhile, heat 2 cups of the ghee in a large heavy pot over medium heat until a slice of the onion sizzles instantly when dropped into the pot. Fry onions, stirring often with a slotted spoon, until dark brown but not burned, about 8 minutes. Drain onions on paper towels. Finely mince onions in a food processor, transfer to a bowl, and set aside. Discard all but 2 tbsp. of the ghee. Blend cashews, charoli nuts, and 1⁄4 cup cold water together in a clean blender until a loose paste forms and set aside. Toast chickpea flour in a large dry skillet over medium-high heat, stirring frequently, until it darkens slightly, about 2 minutes; set aside.
If you choose to give a smoky flavor to the kebabs, spread the meat mixture out in a large skillet or a wide dish with a tight-fitting lid. Make a well in the mixture and set an onion cup in the well. Add a hot hardwood-charcoal coal to the cup, spoon 1 tbsp. of the reserved ghee over the coal (it will immediately begin smoking), and quickly cover skillet or dish. Set aside to let smoke for 10–15 minutes. Discard onion cup, extinguishing coal, if using, in water.
Add coconut, chile powder, garam masala, mace, cardamom, pepper, screw pine water, creams, onions, nut paste, and chickpea flour to meat mixture and mix well with your hands. Wash hands, then grease with remaining reserved gheeand shape meat mixture into 18 1 1⁄2"-wide patties. Fry patties in remaining ghee in a large nonstick skillet over medium heat, turning once and basting often with the ghee, until dark brown and crisp, 4-6 minutes per side. Drain on paper towels. Serve at once.