Heat a large pot over medium-high heat. Add onion, celery, carrots, green bell pepper, red bell pepper, and a splash of vegetable broth. Cook and stir until vegetables are softened, about 10 minutes.
Stir garlic, oregano, cayenne pepper, paprika, salt, and black pepper into the vegetable mixture. Saute until fragrant, about 5 minutes. Add the remaining broth, split peas, sweet potato, and bay leaf. Reduce heat to medium-low. Simmer, covered, until split peas begin to soften and pop, about 45 minutes.
Transfer 1/2 the soup into a blender; puree until smooth. Pour back into the pot and stir well. Pour soup into serving bowls and garnish with green onion.