Heat 1 tablespoon oil in a large saucepan over medium heat. Add the garlic, leek, and ½ teaspoon salt. Cook, stirring occasionally, for 3 minutes.
Add the carrot, celery, zucchini, cannellini beans, and chicken broth. Simmer, covered, until the vegetables are tender, about 15 minutes.
Meanwhile, heat the remaining tablespoon of oil in a medium skillet over medium-high heat.
Season the pork with ¼ teaspoon each salt and pepper and cook until cooked through, 2 to 3 minutes per side.
Shred the pork into pieces and stir into the soup.