To make it by hand, combine the egg yolks, mustard, salt, Tabasco, and vinegar in a medium-size mixing bowl and whisk to blend well. Add the oil, about 2 tablespoons at a time, whisking in between each addition, until thick and smooth.

To make it in a blender or food processor, process the egg yolks for about 30 seconds. Add the mustard, salt, Tabasco, and vinegar. Pulse several times to blend. With the machine running, slowly drizzle in the oil through the feed tube until the mixture thickens.