Preheat oven to 400°.
To prepare dressing, remove white papery skin from garlic heads (do not peel or separate the cloves). Wrap each head separately in foil. Bake at 400° for 1 hour; cool. Cut crosswise, and squeeze to extract garlic pulp to measure 3 tablespoons. Discard skins. Place garlic, mayonnaise, mustard, paste, and black pepper in a food processor; process until smooth. With food processor on, slowly pour vinegar and oil through food chute; process until well-blended.
To prepare salad, cut bell peppers in half lengthwise; discard seeds and membranes. Place halves, skin sides up, on a foil-lined baking sheet; flatten with hand. Broil 15 minutes or until blackened. Place in a zip-top plastic bag; seal. Let stand 15 minutes. Peel; cut into 1-inch strips. Combine dressing, lettuce, 2 tablespoons cheese, and rye bread cubes in a large bowl, tossing gently to coat. Divide salad among 8 salad plates. Arrange bell pepper strips on top of salads. Sprinkle evenly with 2 tablespoons cheese.