In a small bowl combine egg yolk, salt, and lemon juice. Whisk vigorously for 1 minute.
Very gradually whisk in 1/2 teaspoon of the oil at a time. (Do not add more than 1/2 teaspoon at a time!)
Once half of the oil has been incorporated, start adding the oil 1 tablespoon at a time until all of the oil is incorporated and mixture is very creamy and thickened.
Taste, add salt if needed, and serve or store chilled in airtight container up to 1 week.
Serving size: Makes 1/2 cup aioli. For the egg: You really want the egg yolk to be warm, at least room temperature. If you forget to take it out of the fridge in advance, you can speed it up by placing the whole egg in a bowl of hot water for about 5 minutes.