Add eggs, lemon juice, salt, vinegar, and ground mustard to a wide-mouth mason jar. Use an immersion blender to blend until the mixture has emulsified and it starts to look creamy.
With a slow steady stream, add the oil while continually blending and moving the immersion blender around to fully mix. Once all of the oil has been added and the mayonnaise is fully blended, taste and add more lemon, salt, and/or mustard powder if necessary. If the mayo tastes really creamy and oily, generally keep adding more salt and lemon until it tastes like the mayo you’re used to.
Store in an airtight container in the refrigerator.