Using an electric hand mixer, blend together egg yolks, vinegar, and mustard powder. The mixture will become a pale yellow color.
Slowly, and I mean slowly, drizzle one drop of oil at a time while blending.
Once about 1/4 cup of oil has been added the egg yolks will emulsify, you can then add the remaining oil in a very slow stream while continuing to blend.
Storage: Store in a jar with well sealed lid in refrigerator for no more than 5 days.