NOTE: The egg and lemon juice must be at room temperature - it will affect the final outcome! If you have an immersion blender, see note below.
Place the egg and lemon juice in a blender or food processor. Add the mustard, salt, and 1⁄4 cup of the oil and blend for 20 to 30 seconds.
While the blender/ processor is running, slowly drizzle in the remaining 1 cup of oil. This should take a minimum of two minutes.
After a few minutes you’ll start to have something that looks like the consistency of mayonnaise. Exciting stuff!