Place egg, vinegar, lemon juice, salt and pepper in a wide mouth mason jar or a blender. Blend until combined.
With the blender on or with the immersion blender in the jar running, slowly drizzle the oil in until it emulsifies.
Move the immersion blender up and down in the jar until think. This should take less than a minute.
Store in fridge up to two weeks. Makes 1 1/2 cups.