Step 1Heat the oven to 250 degrees. Halve the loaf of bread crosswise. Pull the bread out in 1- to 1½-inch chunks and put the chunks in a large bowl (save the remaining bread and crusts for another use, such as bread crumbs).
Step 2In a sauté pan, combine the oil and anchovies over low heat, breaking up the anchovies with the tines of a fork or a wooden spoon, and cooking until the anchovies have disappeared into the oil, about 5 minutes. Stir in the garlic and cook until it is fragrant, about 1 minute (stir constantly so the garlic does not burn). Remove from heat.
Step 3Sprinkle the salt over the bread and drizzle with the seasoned oil. Toss the bread to coat the pieces evenly. Spread the bread in an even layer onto a rimmed baking sheet and bake until golden, about 30 minutes. Check the bread occasionally, using tongs to turn the pieces for even toasting. Remove any smaller croutons that are browning quickly to a plate, until all of the croutons are toasted. Cool the croutons to room temperature before adding to the salad.
Step 1In the bowl of a food processor, combine the beaten egg yolk with the anchovies and garlic, pulsing to combine. Combine the olive and vegetable oils, and add a few drops of the oil blend to the food processor, pulsing to incorporate it in with the egg. Add the lime juice, vinegar, mustard, Worcestershire, several dashes of Tabasco and salt, pulsing a few times to incorporate the flavors. With the machine running, slowly drizzle in the rest of the oil, forming the dressing (drizzle only a few drops a time at first, increasing little by little as the dressing emulsifies). Stir in the pepper and Parmigiano, and taste the dressing, adjusting the seasoning if desired. This makes about 1½ cups dressing, more than is needed for the remainder of the recipe; the dressing will keep, 3 to 5 days, covered and refrigerated.
Step 1Remove and discard the outer limp leaves from outside the hearts of romaine. Trim and discard the delicate or limp dark green tips of the leaves (about 2 to 3 inches from the top), so that only the sturdy hearts remain; you want only the acid green or yellow hearts, nothing leafy or dark green. (You will chop away more than you feel comfortable throwing away, so find another use for it.) Separate the leaves from the cores, discard the cores and refrigerate the lettuce leaves until ready to assemble the salad.
Step 2To make the salad, put the leaves in a large mixing bowl. Sprinkle the salt and lime juice over the leaves, tossing to coat the lettuce with the seasoning. Drizzle the dressing over the leaves, gently tossing and massaging the dressing over each leaf. Add the croutons and gently toss the salad again.
Step 3Transfer the salad to a large wide-mouthed bowl, building it in layers with grated cheese and pepper between each layer. Grind pepper over the top of the assembled salad and serve immediately.