1. Cut sausages into 1/4-inch-thick slices.
2. In a 6- to 8-quart pan over medium-high heat, stir sausages often until lightly browned, about 10 minutes. With a slotted spoon, transfer sausages to paper towels to drain. Discard all but 1 teaspoon fat from pan.
3. Add onion and garlic to pan. Stir often over medium-high heat until onion is limp, about 5 minutes.
4. Add broth to pan. Tie cinnamon stick, bay leaf, and allspice in cheesecloth and add to broth. Cover and bring to a boil over high heat.
5. Meanwhile, peel potatoes and cut into 1/2-inch cubes. Cut out and discard tough parts of collard stems. Rinse leaves well, drain, and stack. Cut stack in half lengthwise, then cut crosswise into thin strips.
6. Add collard greens, potatoes, and beans to broth; cover and bring to a boil.
7. Simmer, covered, over low heat for 20 minutes. Add sausages and continue simmering, covered, until potatoes are tender when pierced, 5 to 10 minutes longer. Remove and discard wrapped spices.
8. Ladle soup into bowls. Add salt and pepper to taste.