Rinse the romaine leaves well, drain, and tear into large (approximately 3″) pieces. Wrap with a tea towel and refrigerate until needed.
In a frying pan, cook bacon until crisp, drain on a paper towel, and crumble. Set aside.
In the same frying pan used to cook the bacon, pour off all but 1 tablespoon of the bacon drippings and saute the bread cubes until golden and crisp. Set aside on a paper towel.
Mix the oils and heat until very warm.
Prepare the Caesar dressing. You may use a whisk, small food processor, or electric mixer to make the dressing; the technique remains the same, as follows: Place egg yolk, ground mustard seed, garlic, and 2 mashed anchovies in a mixing bowl (or the container of a food processor, as the case may be) and whip until they are well blended and light. While continuing to whip the egg yolk mixture, very gradually (important!) add the heated oil in a very thin, thread-like drizzle (important!) until the mixture thickens to the consistency of mayonnaise and all oil has been incorporated. Add the lemon juice, vinegar, parmigiano-reggiano cheese, and a generous grinding or two of black pepper and mix. Taste the dressing and add more anchovies and seasoning, if needed, to suit your taste. Set aside (in the refrigerator if you will not be serving the salad immediately).
Place the romaine greens in a large salad bowl. Add the dressing mixture and toss until the greens are well coated. Sprinkle on the bacon and croutons. Toss again. Serve immediately.