Sausages with white beans

Sausages, any kind you like, but preferably NOT Italian.  I used one the butcher called Toulouse.
White beans, fresh or dried
One large carrot cut in chunks
One small onion, quartered
One bay leaf
6 cloves of garlic
Red wine vinegar
Salami cut into matchsticks
Red onion slivered

The white bean part of this takes time, but can be done on different days.  Two days ago I shelled a bag of white beans that my husband got at the farmers market.  I think they were cannelini, but any any white bean would do.  If you don’t have fresh beans, soak a bag of dried for a few hours.  Cover the beans with cold water and bring to a boil with the carrots, onion and bay leaf.  Lower the heat and keep at a high simmer until cooked through.  To test, cut a bean in half.  It should be a uniform color all the way through, no white chalky center.  When the beans are done, turn them off and salt the water and add a tablespoon or two of olive oil.  Let cool then cover and store in the refrigerator in the cooking liquid.  They keep up to 4 days.
The day you want to eat the beans, remove the onion and carrots and bay leaf from the bean.  Add 5 peeled cloves of garlic that you’ve smashed with the back of a chef’s knife.  Bring back to a boil and simmer until the garlic is soft.  Drain the beans and garlic and toss with red wine vinegar to taste (I add 1/2 a cup) and one clove of chopped garlic.  Let cool to room temperature than mix in salami and red onion.
Fry the sausages or grill them or however you like to make them and serve with the beans.