First, make the dressing. In a bowl, whisk together the egg yolks, lemon juice, mustard powder, Worcestershire sauce, and pepper sauce. Whisking continuously, gradually whisk in the vegetable oil and then the olive oil, a little at a time, until the dressing forms an emulsion.
If it is too thick, whisk in a little cold water. Place about half of the dressing in a large bowl, then add the lettuce leaves, croutons, and half of the Parmesan.
Toss gently to coat the leaves. Lay out the leaves on serving plates or a platter, and top with the chicken and anchovies. Sprinkle with the remaining Parmesan, drizzle with some more of the dressing, and serve. Instead of chicken, use large shrimp, cooked and peeled, with tails left on.
If you don't have time to make your own Caesar dressing, some good varieties can be found on supermarket shelves.