Preheat oven to 450 degrees. Combine the butter and olive oil in a large bowl. Add the cubes of bread, and toss until coated. Sprinkle with salt, cayenne pepper, and black pepper; toss until evenly coated. Spread the bread in a single layer on a 12-by-17-inch baking sheet. Bake until croutons are golden, about 10 minutes. Set aside.
Place the garlic, anchovy fillets, and salt in a wooden salad bowl. Using two dinner forks, mash the garlic and anchovies into a paste. Using one fork, whisk in the pepper, lemon juice, Worcestershire sauce, mustard, and egg yolk. Whisk in the olive oil.
Chop the romaine leaves into 1- to 1 ½-inch pieces. Add the croutons, romaine, and cheese to the bowl, and toss well. If you wish, grate extra cheese over the top. Serve immediately.
