Heat oil in a large stockpot over medium-high heat. Cook onion for 2-3 minutes until translucent, then add garlic and cook another 30 seconds.
Stir in curry paste and cumin and toast for 30 seconds, then add sweet potato and saute for 3 minutes.
Add chicken broth and coconut milk, scraping the bottom of the pot. Bring to a simmer and cook sweet potato until soft, about 20 minutes.
While sweet potato is cooking, roast the red bell pepper under the broiler, turning so all sides are slightly charred. Immediately seal in a plastic bag and let steam until skin slides off easily then finely dice the peeled pepper.
When sweet potato is fully cooked, puree with an immersion blender or in an upright blender and return to the pot. Stir in roasted pepper and crab meat and simmer for about 3 minutes.
Salt to taste and serve hot!