In a small food processor or using the small bowl attachement of your large food processor, add the egg, the mustard, apple cider vinegar, and salt and process for 30 seconds.
1 large egg, 1/2 tbsp mustard, 1 tbsp apple cider vinegar, 1/4 tsp salt
Scrape down the sides of the food processor bowl, turn on the food processor again and slowly start adding the oil. You want to go as slow as possible to allow your mayonnaise to emulsify. Once the mayonnaise mixture start to thicken a little more, you can start adding your oil a little faster.
1 cup oil
Wait 10 seconds after adding the last bit of your oil, then turn off the food processor, scrape the sides, taste the mayo, and add any salt or lemon juice to taste and process for another 10 seconds.