Place cranberry beans into a large container and cover with several inches of cool water; let soak, 8 hours to overnight. Drain.
Shred carrot, yellow onion, celery, and red pepper in a food processor to create a sofrito mixture.
Heat oil in a 7-quart pressure cooker over medium-high heat. Add sofrito mixture and saute until softened, 3 to 5 minutes. Add soaked beans, potatoes, diced carrots, zucchini, pumpkin, and diced onion. Cook and stir until warmed through, 3 to 5 minutes more. Add oregano, rosemary, and bay leaf. Stir well to coat vegetables with oil and seasonings.
Add enough broth to cover vegetables by 1 inch. Close the pressure cooker lid and bring up to pressure, about 10 minutes. Cook an additional 10 minutes from the first whistle.
Allow pressure to release naturally and remove lid, about 10 minutes. Taste and adjust salt if necessary. Add additional broth to allow for cooking the pasta. Bring to a boil and add pasta. Cook, stirring occasionally, until tender but still firm to the bite, about 8 minutes. Add more boiling broth if needed during cooking.
Ladle soup into bowls and top with minced hot pepper and Parmigiano-Reggiano cheese.