On a very clean work surface and using a sharp knife, slice beef into thin slices no thicker than ¼ inch. Then cut into thin ¼- or ⅛-inch stips. Cut strips crosswise into a fine mince. Transfer to a mixing bowl.
Add mayonnaise and season with salt and pepper to taste, stirring well to combine thoroughly. If needed add additional olive oil, vinegar, and/or mustard in very small increments to adjust flavor to taste (depending on your mayonnaise, you may not need any, or you may find the beef needs a little more to get the flavor just right). If desired, mix in the drops of fish sauce.
Add shallot, chives, parsley, cornichon, and capers and stir until thoroughly combined.
Mound steak tartare on a serving plate (you can use a ring mold to make a perfect circle, if desired). Top with egg yolk, if using, and serve right away with toasts and additional cornichons on the side.
