In a 6-quart (or larger) Dutch oven over medium heat, cook the bacon, stirring occasionally, until partially crisp, about 7 minutes. With a slotted spoon, transfer the bacon to a paper-towel-lined plate. Add the onions to the pot and cook, scraping up any browned bits and stirring occasionally, until softened, 6 to 8 minutes. Add the garlic and rosemary and cook, stirring constantly, until fragrant, about 1 minute. Add the chicken broth, chickpeas, tomatoes and their juices, carrots, celery, cinnamon stick, 3/4 tsp. salt, 1/2 tsp. pepper, and 1 cup water. Bring to a boil over high heat; skim any foam as necessary. Reduce the heat and simmer, stirring occasionally, until the carrots and celery are very tender, about 30 minutes.
Meanwhile, cook the tubettini according to the package directions and drain.
Discard the cinnamon stick and add the pasta. Stir in the bacon and vinegar. Season to taste with salt, pepper, and more vinegar. Serve garnished with the Parmigiano-Reggiano.
You can store leftovers in the refrigerator for up to 2 days.