1. In a medium saucepan set over medium-high heat, cook the bacon pieces, stirring frequently, until brown and just crisp, about 5 minutes. Remove from heat. Using a slotted spoon, transfer bacon to a paper-towel-lined plate; set aside.

2. Pour all but about 1 tablespoon of bacon fat from the pan. Return the pan to the heat; add the onion, carrots, and celery. Cook, stirring occasionally, until the vegetables begin to soften, about 3 minutes. Add the stock and 2 cups water, and bring to a boil. Reduce heat to medium, and simmer until the vegetables are tender, about 15 minutes. Add the beans, sage, salt and pepper, and half of the reserved bacon. Simmer for a few more minutes while preparing the cheese toasts.

3. Meanwhile, heat the broiler; place bread on a baking sheet. Sprinkle bread with cheese; broil until cheese is melted and bread is just golden, about 2 minutes. Cut into triangles.

4. Garnish soup with remaining bacon, and serve with cheese toasts on the side.