Food Processor: Add egg, mustard, salt, vinegar and lemon juice to the food processor bowl. Pulse 10-12 times to mix ingredients well. Pour oil into the food pusher tube while the food processor is running. Put mayo in a glass container and store in fridge, it will thicken up even more once it is cold.
Immersion Blender: Add all the ingredients the immersion blender cup or another similar container. Hold immersion blender on the bottom just over the egg and pulse several times until egg emulsifies. Slowly bring the immersion blender up and down to incorporate oil until mayo is thick. Store in refrigerator.
Blender or Whisk: Add egg, mustard, salt, vinegar and lemon juice to bowl or blender. Mix until combined well. Very slowly add the oil while constantly mixing. Drop by Drop at first and as it emulsifies and comes together you can increase to a very slow stream. This process will take about 10 minutes. Store in glass container in refrigerator.
