Heat oven to 425°F. Toss cabbage with 1 tablespoon oil on sheet; roast 20 to 25 minutes, turning once, until tender with browned edges.
Heat remaining tablespoon oil in soup pot over medium. Soften onion 6 to 7 minutes; stir garlic, paste, marjoram, and paprika 1 minute.
Add broth and drained sauerkraut; gently simmer partly covered 15 minutes.
Fold in roasted cabbage, ham, and pepper; simmer 5 to 7 minutes until ham 165°F. Stir gently to keep larger cabbage pieces intact.
Divide among six bowls with both cabbages and ham in each.