Place a mixing bowl on top of a towel on your countertop. This will help secure the bowl while whisking.
In a bowl, add egg yolk, mustard, and salt and pepper to taste.
Whisk together ingredients until combined.
Slowly add oil, whisking as oil is added.
The mayonnaise should begin to take form, continue whisking and adding all of the oil slowly.
Once you have used all the oil, add a 1/2 tbsp of white vinegar, whisking into mayonnaise.
This final result should be a thick and creamy mixture.
Add more salt & pepper to desired taste if necessary.