Heat a large skillet over medium heat. Add ground beef and cook, stirring occasionally and breaking into crumbles, until no longer pink, about 10 minutes.
Remove meat to a paper-towel lined plate. Press additional paper towels on top of meat to further reduce fat.
Discard all but 1 tablespoon of fat in skillet. Add sweet potato, onion, bell pepper, and curry powder. Cook, stirring occasionally, until onion is crisp-tender, about 5 minutes.
Stir in flour and cook for about 1 minute.
Add broth or water, black-eyed peas, and coconut milk. Bring to a boil, then reduce heat. Cover and simmer until sweet potato is tender, about 10 minutes.
Stir in spinach and thyme. Cook until spinach wilts, about 1 minute.
Season with salt and pepper to taste.