Heat oven to 400°F. Cut garlic top to expose cloves; drizzle with oil and wrap in foil. Roast 40 to 45 minutes until soft; cool 10 minutes.
Meanwhile, toss cabbage with vinegar, sugar, and its salt. Rest 20 minutes, turning once; drain thoroughly and squeeze lightly.
Squeeze garlic into a food processor. Add beans, yogurt, lemon juice, spread salt, and pepper; blend smooth, scraping as needed.
Broil only cut bagel faces 1 to 2 minutes; cool. Spread garlic-bean mixture evenly on both cut faces.
Loosely fold beef onto four bottoms; divide drained cabbage over it. Close, halve, and serve cold; refrigerate unused sandwiches.