Preheat the oven to 350 degrees F (175 degrees C).
Toss baguette cubes with olive oil, 1/4 teaspoon salt, and 1/4 teaspoon pepper, in a large bowl. Place on a baking sheet.
Place a wire cooling rack on a separate baking sheet; lay bacon slices on top.
Bake bacon and baguette cubes in the preheated oven until bacon is browned and baguette is toasted, about 15 minutes; make sure to turn the bread halfway through. Remove from oven and let cool to room temperature. Finely chop bacon.
Mash anchovy fillets, garlic, and mustard together with a fork in a large salad bowl. Add mayonnaise, 1/2 of the Parmigiano-Reggiano cheese, lemon juice, Worcestershire, and season with salt and pepper. Whisk dressing until well combined.
Shave Brussels sprouts using a mandolin; place into the bowl with the dressing. Add 1/2 of the bacon and croutons; toss until well coated. Serve with remaining Parmigiano-Reggiano cheese, croutons, and bacon on top.