Heat the vegetable oil in a large pot or Dutch oven over medium heat. Add the chopped onions and minced garlic to the pot and sauté until the onions become translucent, about 5 minutes.
Add the chopped bell peppers and tomatoes to the pot. Sauté for another 5 minutes until the vegetables soften.
Transfer the sautéed vegetables to a blender or food processor and blend until smooth. If needed, add a splash of water to achieve a smooth consistency.
Return the blended mixture to the pot and stir in the tomato sauce, vegetable broth, paprika, thyme, curry powder, cayenne pepper, and salt. Mix well.
Bring the stew to a simmer and let it cook uncovered for about 20 minutes, stirring occasionally to prevent sticking.
Add the cooked beans to the pot and stir to combine. Let the stew simmer for an additional 10 minutes to allow the flavors to meld together.
If using, add the chopped spinach or ugu leaves to the pot and stir until wilted.
Taste the stew and adjust the seasoning if needed.
Serve the Buka Stew hot with your choice of accompaniments, such as boiled plantains, yam, or rice.