Melt butter in a medium pot over medium heat. Add pancetta; cook and stir until browned, about 3 minutes.

Remove pancetta but leave grease in the pot. Add onion, carrots, and celery. Saute until fragrant, about 3 minutes. Stir in garlic and cook for 30 seconds. Pour in white wine and bring to a boil while scraping up any browned bits from the pot with a wooden spoon. Boil until reduced by half, 6 to 8 minutes.

Add in cannellini beans, chicken stock, Parmesan cheese, cream, rosemary, oregano, red pepper flakes, bay leaf, salt, and pepper. Increase heat to high and bring to a boil. Reduce heat to a simmer. Cook, stirring every so often to avoid burning, until the cheese and starch in the beans have thickened the liquid to a sauce-like consistency, 45 minutes to 1 hour.