Fill a large pot with lightly salted water and bring to a rolling boil. Stir in tubettini and return to a boil. Cook uncovered, stirring occasionally, until tender yet firm to the bite, about 9 minutes. Drain and set aside.

Meanwhile, turn on a multi-functional pressure cooker (such as Instant Pot) and select Saute function. Add pancetta and cook until fat has been rendered, about 5 minutes. Add onion, carrots, and celery; saute, stirring frequently, until translucent, about 4 minutes. Add garlic and cook for 1 minute.

Pour 1/4 cup chicken broth into the pressure cooker and bring to a boil while scraping the browned bits of food off the bottom with a wooden spoon. Add remaining chicken broth, cranberry beans, diced tomatoes with juice, bay leaves, salt, and pepper.

Close and lock the lid of the pressure cooker and close the valve. Select Manual pressure according to manufacturer's instructions; set timer for 45 minutes. Allow 10 to 15 minutes for pressure to build.

Release pressure using the natural-release method according to manufacturer's instructions, about 10 minutes. Unlock and remove the lid.

Transfer 2 cups of soup, with as many beans as possible, to a mini food processor; blend until smooth. Place back into the pot and stir. Ladle soup into bowls, add the reserved pasta, and serve.