Heat a large saucepan over medium-high heat. Cook onion in oil until softened.
Peel sweet potato if desired. Cut into 1/2 chunks. Add broth,sweet potato, and pasta. Bring to a boil over high heat, reduce heat and simmer uncovered 10-15 minutes until potatoes and pasta are nearly cooked.
Stir in tomatoes, beans, and greens. Return to a simmer and cook until sweet potatoes and greens are tender.
Stir in paprika (or red pepper flakes), vinegar, honey, and pepper. Keep warm until ready to serve.
Reheats well. Leftover soup may be covered and refrigerated up to three days or frozen up to three months.