Heat the olive oil in a large Dutch oven or heavy pot over medium heat. Add the diced pancetta and cook, stirring occasionally, until the fat has rendered and the pancetta is golden and crispy, about 5–6 minutes. Remove with a slotted spoon and set aside, leaving the rendered fat in the pot.
Add the onion, carrot, and celery to the pot. Season lightly with salt and pepper. Cook over medium heat, stirring often, until the vegetables are softened and the onion is translucent, about 6–8 minutes. Stir in the minced garlic and tomato paste, cooking for 1 minute until fragrant and the paste coats the vegetables.
Pour in the crushed tomatoes, chicken broth, and add the bay leaf, rosemary sprig, and Parmesan rind. Bring to a boil over high heat, then reduce to a vigorous simmer. Cook for 10 minutes, stirring occasionally, to let the flavors meld.
Stir in the drained cannellini beans and the ditalini pasta. Continue to simmer, stirring occasionally, until the pasta is al dente and the beans are heated through — about 8–9 minutes. The soup will thicken; if it becomes too thick, add a splash of broth or water to reach desired consistency.
Remove the pot from heat. Discard the rosemary sprig, bay leaf, and Parmesan rind. Stir the reserved crispy pancetta back into the soup. Ladle into warm bowls, drizzle generously with extra-virgin olive oil, and top with plenty of grated Parmigiano-Reggiano and a pinch of crushed red pepper flakes, if desired.