Combine the egg yolk, egg, mustard and two tablespoons of lemon juice in the bowl of a food processor or blender. Add a pinch of salt and pepper and process for 1 minute.
Scrape down the side of the bowl, and with the motor running, dribble in the oil as slowly as possible, starting with just a few drops in a steady stream. It should take 8–9 minutes to add all of the oil to the processor.
When finished, the mayonnaise should be thick and silky. Shut the motor off and scrape down the sides of the bowl. Season with salt and pepper, to taste, and add an additional tablespoon of lemon juice if you think it needs more acidity.
Store in a lidded container in the fridge for up to one week.
Add 1–2 minced garlic cloves per cup of mayonnaise for a garlic-infused version.
Add ½ cup finely chopped pickles to make homemade tartar sauce.
Combine 1 cup of mayonnaise, the juice of 1 lime and 2–4 tablespoons of chopped cilantro for quick and easy cilantro mayonnaise.
Add ½ cup pesto to 1 cup mayonnaise for a pesto sauce perfect for pasta salad or slathering on burgers.