In a large glass bowl, whisk together the egg yolk, mustard, sea salt and sugar (if using).
In a small bowl, stir together the vinegar and lemon juice. Whisk half of the vinegar mixture into the egg mixture until thoroughly combined.
Start whisking briskly, then begin adding the oil a few drops at a time, until the liquid begins to thicken and lighten a bit. Once you reach that point, continue whisking while you add the oil in a very slow, steady stream. Once half of the oil has been incorporated, whisk in the remaining vinegar mixture. Continue whisking until all of the oil is incorporated.
Allow the mixture to sit at room temperature for 1 to 2 hours, then refrigerate for up to 1 week.
Notes
Note: If you have an aversion to raw eggs or are pregnant, substitute pasteurized eggs. You can usually find these in regular grocery stores; Davidson's is a popular pasteurized brand.Nutritional values are based on the whole recipe