Heat oven to 375° F. Toss the bread, 3 tablespoons of the oil, and ¼ teaspoon each salt and pepper on a rimmed baking sheet. Bake, tossing once, until the bread is golden brown, 20 to 25 minutes. Let cool.
Meanwhile, on a second rimmed baking sheet, toss the shrimp, 1 tablespoon of the remaining oil, and ¼ teaspoon each salt and pepper. Bake until the shrimp are opaque throughout, 4 to 6 minutes. Let cool.
Whisk the mayonnaise, lemon juice, mustard, anchovies (if desired), Worcestershire sauce, garlic, ¼ cup of the Parmesan, the remaining 2 tablespoons of oil, and ½ teaspoon pepper in a large bowl. Add the romaine, shrimp, croutons, and the remaining ¼ cup of Parmesan and toss to combine. Serve immediately.