Add the ham bone, vegetables, diced tomatoes, herbs/seasonings, and liquid (broth and water) to the Dutch oven.
Boil for 20 minutes and then discard the ham bone.
Add the tomato sauce and return to a low simmer.
If using tomato paste to thicken, slowly add a tablespoon or so at a time until the broth reaches the desired thickness.
Add the ham and bean and return to a low simmer for 10 minutes.
Serve and enjoy.
Notes
Do not skip the boil. The 20-minute boil with the ham bone extracts collagen and gelatin, giving the broth real body. A gentle simmer will not do the same thing.
Taste before salting. Ham, canned broth, and canned tomatoes all carry sodium. You may not need any extra salt at all. Always taste first and adjust from there.
Thicken with tomato paste gradually. Add a tablespoon at a time and stir until you reach the consistency you want. You can always add more, but you cannot take it out.
Add beans last. Canned beans are already cooked. Simmering them too long makes them mushy. Five to ten minutes to heat through is all they need.
Bouillon swap: Water plus Knorr chicken bouillon works just as well as boxed broth. This is actually what we use most of the time.