Heat the olive oil in a large Dutch oven over medium-high heat. Add the pork pieces and brown them on all sides, about 6 to 8 minutes. Season with salt and pepper as they cook.
Add the onion, carrots, and minced garlic to the pot. Cook for 3 to 4 minutes until the onion softens.
Sprinkle the flour over the mixture and stir for 1 minute to form a light roux that will thicken the gravy.
Slowly pour in the chicken broth while stirring to avoid lumps. Add the rosemary sprigs and bring the stew to a simmer.
Reduce the heat to low, cover, and cook for 45 minutes until the pork is tender.
Stir in the rinsed white beans and simmer uncovered for 10 more minutes so the beans warm through and the gravy thickens further. Remove the rosemary sprigs before serving.