Cover bean mix with soaking water and refrigerate for 8 to 12 hours, then drain and rinse; preparation time includes an 8-hour soak. Put beans in a large pot with the fresh boiling water.
Bring to a full rolling boil and maintain that boil for 30 minutes, adding some of the measured 2 cups additional hot water if needed to keep beans submerged. Drain and rinse, then return beans to the pot with the measured broth.
Simmer partly covered for 60 to 90 minutes until the largest beans are fully tender, checking several types and adding up to the measured cup of hot water if the broth drops too low.
Meanwhile, heat oil in a skillet over medium heat. Cook onion, celery and carrot for 7 minutes, add garlic, paprika and oregano for 1 minute, then add tomatoes and roasted pepper and simmer for 5 minutes.
Fold the tomato mixture, ham and black pepper into the tender beans. Simmer for 15 minutes until the ham reaches 165°F and the broth is lightly thickened by the softer beans.
Stir in vinegar and taste before adding up to the measured salt. Divide among eight bowls, keeping a mixture of beans and ham in each serving.