Place ½ cup of oil in a food processor, then add the eggs, ground mustard, and salt.
Process thoroughly, for about 30 seconds, until combined and pale yellow in color.
With the food processor running, slowly drizzle in remaining oil until mixture is emulsified and thick, about 60-90 seconds.
With the food processor still running, add the lemon juice, and mix briefly, about 5-10 seconds, until incorporated.
Transfer homemade mayo to a container with a lid until ready to use. Store in refrigerator for up to 4 days.
Enjoy with your favorite sandwiches or use as the base for other favorite sauces and spreads.
A few suggestions: