Mix tamarind concentrate, if using, with 2 tbsp. hot water (if using lime juice instead, add just before serving). Put tamarind, onion, ginger, coriander, minced chiles, turmeric, cayenne, 1 tsp. salt, and the coconut milk in a blender and whirl until very smooth.
Pour coconut milk mixture and 1 cup water into a wide, deep pot and bring to a simmer. Add potatoes, halved chiles, and carrots; cover and simmer, stirring occasionally, until tender, about 20 minutes.
Add fish, spinach, and curry leaves and simmer until fish chunks are opaque all the way through, about 5 minutes. Stir in peas, simmer 1 minute, and season with salt to taste and lime juice, if using.
*Available at South Asian markets.
Note: Nutritional analysis is per serving.