Add eggs, dijon mustard, vinegar, and salt into a mixing bowl. Gently puree with an immersion blender until smooth.
Once everything else is fully blended, slowly start adding the olive oil, continuously blending on low speed the entire time. Important: pour the oil slowly! It should take 3-5 minutes to pour out all of the oil, stirring all the while.
Slowly, the emulsion will thicken and you will reach the desired texture. Remove from bowl; store in an airtight container and refrigerate until ready to use. Use mayonnaise as the base to numerous aiolis (mayonnaise-based sauces) or as a condiment to your favorite sandwich.