Place black beans into a large container and cover with several inches of cool water; let stand 8 hours to overnight. Drain beans and rinse with fresh water.
Heat oil in a large Dutch oven or stockpot over medium heat; cook and stir yellow onion, paprika, and cumin seeds until fragrant, about 3 minutes. Add red bell pepper, green bell pepper, garlic, oregano, and bay leaves; cook and stir until onion is translucent and bell peppers are tender, 6 to 8 minutes.
Mix vegetable stock, black beans, tempeh, rum, and jalapeno pepper into onion mixture. Increase heat to medium-high, bring to a simmer, reduce heat to medium-low, and cook until beans are tender, about 45 minutes.
Pour water into bean mixture; season with 1 1/2 teaspoons salt. Cook, stirring occasionally, until beans begin to fall apart and soup thickens, 30 to 40 minutes; season with salt and pepper. Remove and discard bay leaves from soup.
Ladle soup into bowls and garnish with hard-boiled eggs and red onion.