1. Place beans in a Dutch oven; cover with 6 cups boiling water. Let stand for 1 hour; drain.
2. Preheat oven to 325°.
3. Heat a Dutch oven over medium-high heat. Add 1 tablespoon olive oil to pan, and swirl to coat. Sprinkle pork evenly with 1/4 teaspoon salt and pepper. Add pork to pan; sauté for 6 minutes, turning to brown on all sides. Stir in beans, remaining 1/4 teaspoon salt, broth, and next 3 ingredients (through sage); bring to a boil. Cover and bake at 325° for 1 hour.
4. Heat a skillet over medium-high heat. Add remaining 1 1/2 teaspoons oil to pan; swirl to coat. Add onion and carrot; sauté 4 minutes, stirring occasionally. Add garlic, and sauté 1 minute, stirring constantly. Stir onion mixture into bean mixture; bake at 325° an additional 1 1/2 hours or until beans are tender. Drain solids through a sieve over a bowl, reserving solids and cooking liquid. Skim fat from top of liquid; discard fat. Stir cooking liquid back into pork mixture.