Heat a heavy pan over medium-high heat. Place chiles in the pan and toast, turning often, until fragrant, 2 to 4 minutes. Transfer toasted chiles to a blender.
Add coconut, rice flour, gram flour, and tamarind to the blender with the chiles and process to a fine paste. Add a small amount of water if necessary.
Heat 2 tablespoons oil in a skillet over high heat. Add coriander, urad dal, and asafoetida; cook and stir for 30 seconds. Transfer this mixture to the tamarind mixture in the blender. Blend to combine.
Place shredded cabbage in a large bowl and add tamarind-coriander paste. Stir to combine; season with salt and sugar.
Heat oil for frying in a large heavy skillet. Spread small portions of cabbage mixture in the hot pan and fry patties until browned, 2 to 3 minutes per side.
