Drop the garlic halves through the opening in blender lid with blender on; process until minced. Add mayonnaise and the next 5 ingredients (mayonnaise through pepper); process until well-blended. Cover and chill at least 1 hour.
Combine oil, Cajun seasoning, and minced garlic in a medium microwave-safe bowl. Microwave at high for 20 seconds. Add bread cubes; toss gently to coat. Spread bread cubes in a single layer on a baking sheet; bake at 400° for 15 minutes or until golden brown.
Place lettuce in a large bowl. Add dressing; toss gently to coat. Sprinkle with cheese, and top with croutons.