Pat fish dry and season with smoked paprika and black pepper.
Heat a cast iron skillet with 1 1/2 tablespoons oil. Once hot, place tilapia filets in the skillet. Allow fish to cook until flesh is opaque and white, 3 to 4 minutes per side. Remove from skillet and set aside.
For broth, heat a Dutch oven with remainder of the oil (you may need to adjust a little). Add onions, celery, bell peppers, garlic, ginger, tomatoes, potatoes, and carrots to the pot. Sprinkle 1 tablespoon curry powder on the veggies and mix well. Cook vegetables until some are just beginning to soften, 3 to 5 minutes. Potatoes and carrots will still be firm at this point.
Add coconut milk, mix well, and allow to simmer for 5 minutes. Add broth, fish sauce, and more curry powder (to taste); mix well and reduce heat to low-medium, cover, and simmer for 5 minutes.
Stir well and taste the broth. If broth needs more curry or possibly a little salt, season to taste.
Reduce heat further to a definite low heat, add mushrooms, cover, and allow to simmer until potatoes and carrots are tender, 5 to 10 minutes. Remove from heat.
To serve, place a piece of fish in a shallow bowl and ladle soup broth on top of the fish.
