I have been making fresh mayonnaise for many years. HIstorically it was made by the father of the family every Sunday in France. It was made by hand and was very labour intensive. It can be made in a blender or food processor which is much easier, but I find it harder to clean up. I make it with a hand blender. It is made right in the jar in which I store it. Quality is very good and cleanup is a snap. You can substitute lemon juice for the vinegar but it won't keep as long.
YOU CAN SUBSTITUTE OLIVE OIL FOR THE VEGETABLE OIL, BUT IT WILL ADD A STRONG FLAVOUR. YOU MAY ALSO SUBSTITUTE LEMON JUICE FOR THE VINEGAR BUT YOU WILL HAVE TO USE UP THE MAYONNAISE MORE QUICKLY. LEMON JUICE DOES NOT KEEP AS LONG AS VINEGAR.
In a pint or quart jar put the egg, salt, mustard, paprika, vinegar and 1/4 c. of the oil.
Blend with your stick blender for a couple of seconds and then start adding the rest of the oil to the jar in a very slow stream and move the stick blender up and down slowly to blend the mixture. The mixture will thicken very quickly as you blend it. It is critical that the oil be added very slowly or the mayonnaise will break and you will have an unusable mess.
Store in the fridge. Will keep for a couple of weeks.