Combine vinegar, lime juice, dry mustard, Tabasco sauce, and salt in the container of a blender. Pulse to combine well.
Add the egg yolk, then allow the blender to run at a medium speed.
Open the top feed hole of the blender, and slowly begin to trickle the olive oil into the spinning blades of the blender. Do not add the olive oil too quickly. The mayonnaise will thicken into a heavy creamy texture once you have added enough olive oil, you may not need to full amount to reach the desired consistency.