Preheat oven to 400°F. Line a large, shallow baking sheet with foil. Add bread cubes to pan, drizzle with 2 Tbsp. olive oil, season with pepper and toss well. Bake until lightly toasted, 8 to 10 minutes. Let cool.
Mash garlic and anchovies in a large salad bowl with 2 forks to make a coarse paste; season with salt. Whisk in vinegar, lemon juice, mustard and Worcestershire sauce; season with pepper. Whisk in remaining 4 Tbsp. oil until well blended.
Add lettuce to salad bowl and toss well. Sprinkle cheese and croutons on top and toss well again. Serve in salad bowls or plates.