In a 4-quart Dutch oven cook onion in hot oil over medium heat for 8 to 10 minutes or until very tender, stirring occasionally. Stir in garlic.
Stir in tomatoes, black-eyed peas, lima beans, the water, chili powder, paprika, and salt. Bring to boiling; reduce heat. Simmer, covered, for 10 to 15 minutes to blend flavors. If desired, top each serving with cheese.