Put eggs, 3 tablespoons oil (from the 2 cups), salt, pepper, and mustard into blender and mix thoroughly on a low setting.

Open the lid to the blender and slowly pour the remainder of the oil into the blender while blender is mixing.

At the end add the vinegar. You might have to stir it in a bit to help the blender mix it. Your mayo should already be thick when you add the vinegar.