Cover beans with soaking water; refrigerate 8 to 12 hours. Drain; rinse. Prep time includes 8-hour soak. Put in large pot with fresh boiling water.
Maintain full rolling boil 30 minutes, adding some measured 2 cups hot water as needed to submerge beans. Drain, rinse, and return with measured broth.
Simmer partly covered 60 to 90 minutes until largest beans fully tender, checking several types. Add up to measured cup hot water if broth low.
Meanwhile, heat oil in skillet over medium. Cook onion, celery, and carrot 7 minutes; add garlic, paprika, and oregano 1 minute. Add tomatoes and roasted pepper; simmer 5 minutes.
Fold tomato mixture, ham, and black pepper into tender beans. Simmer 15 minutes until ham 165°F and softer beans lightly thicken broth.
Add vinegar; taste before adding up to measured salt. Divide among eight bowls with mixed beans and ham in each.