Make the sauce by melting butter in a skillet. Cook shallots and mushrooms until soft and golden, about 10 minutes. Add cilantro stems and 1/2 the leaves, jalapeno peppers, and cumin, lower heat and cook for 5 minutes. Add chicken stock. Turn heat to high and cook until liquid is reduced by half. Add cream and return to a boil. Remove from heat. Puree in a blender, strain, and return to heat.
Whisk egg yolks, sugar, and vinegar together in a small bowl. Pour one cup pureed sauce into egg mixture to temper. Then combine egg mixture and puree, and cook over low heat, stirring constantly, until sauce is thick and smooth. Keep warm.
Preheat broiler or prepare grill. Season chicken lightly with salt and pepper, since sauce will be spicy. Mix oil and lime juice in a small bowl and brush chicken and scallions with it.
Broil or grill thighs about 12 minutes, breasts about 9 minutes, and scallions about 2 minutes per side. Always grill chicken skin-side down first.
Arrange grilled chicken over a bed of Basmati Rice and spoon sauce over all. Garnish with the remaining cilantro leaves and scallions, and serve immediately.
c.1997, M.S. Milliken & S. Feniger, all rights reserved