Heat vegetable oil in a large pot or skillet over medium heat.
Add the chopped onion and minced garlic to the pot and sauté until the onion is translucent.
Add the sliced red and green bell peppers, carrot, potato, cauliflower, and green peas to the pot. Cook for about 5 minutes, stirring occasionally, until the vegetables start to soften.
In a small bowl, whisk together the coconut milk, tomato paste, curry powder, paprika, cumin, coriander, turmeric, salt, and pepper.
Pour the coconut milk mixture into the pot with the vegetables. Stir well to combine.
Bring the mixture to a simmer and let it cook for about 15 minutes, or until the vegetables are tender and the flavors are well blended.
Taste and adjust the seasonings as needed.
Remove from heat and garnish with fresh cilantro or parsley if desired.
Serve the Nigerian Coconut Curry hot with cooked rice or naan bread.