You definitely can use an immersion blender, especially if you are making a smaller quantity of the mayo, which would be easier to do in the cup of an immersion blender. To do this, put the mayo ingredients in the cup of an immersion blender or in a small cup. The blade should be immersed in the ingredients. Place the head of the immersion in the bottom of the cup and turn the blender on at high speed. Blend until the mayo forms. If using a food processor, follow the same procedure as you would with a regular blender. Again, make sure that the blades are immersed in the liquid, otherwise double the recipe.