Heat the oil in a 4 1/2 qt Dutch oven or soup pot over medium-high heat. Peel and coarsely chop the onion, additing it to the pot as you chop. Rinse and dice the celery, adding it to the pot as you dice. Cook, stirring frequently, until the onion begins to brown, about 3 minutes. Meanwhile, pour 1 can navy beans into a colander, rinse well and set aside to drain.
Stir the garlic into the onion mixture. Add the broth and the tomatoes with their juices. Increase heat to high. Add the remaining can of beans with its liquid along with the rinsed beans, bay leaf, thyme and pepper. Stir and cover the pot. When the soup comes to a boil, reduce the heat to low. While the soup is heating, cut the sausage in half lengthwise. Cut the pieces into 1/4", crescent-shaped slices and add them to the pot.
Stir the soup, re-cover the pot and cook at a slow simmer 7-10 min to let the flavors develop. To serve, discard the bay leaf and ladle the soup into bowls. The soup can be made up to 3 days ahead.