Place the egg yolks in a blender. Give them a quick pulse so they are combined. Add in the Dijon mustard and lemon juice and pulse again.
The first 1/3 cup of oil is the most important part of incorporating it into the yolks. It is important to take your time here, otherwise the mixture might split.
Drop by drop, add in the oil, blending thoroughly between each addition. If your blender has a removable section in the lid, you can keep your motor running while you add the oil. However, pay attention to the heat generated by the motor as you don’t want it cooking the eggs.
Once the first 1/3 cup of oil has been incorporated, you won’t be at such a risk of separating the mixture and can start pouring it in a thin, steady stream. The mixture will thicken and start looking like mayonnaise.
Once all of the oil has been incorporated, add in 2 tablespoons of boiling water, blending quickly so it incorporates and doesn’t cook part of the mixture. This, along with the lemon juice and mustard, will help keep the mixture stable. Taste and add salt and pepper as you like. You may also like to add in more lemon juice or mustard at this stage.
Remove the mayonnaise from the blender and store it in a sterilized jar. Check the expiration date of your eggs, as this will be the same expiration date of your mayonnaise. You may like to write this date on your jar to help you remember. Keep refrigerated.