In a clean mixing bowl, whisk together the egg yolk and Dijon mustard until well combined. Slowly add the oil a few drops at a time while continuously whisking to start emulsifying the mixture. As the mixture begins to thicken, gradually increase the oil flow to a thin, steady stream, whisking constantly. Once all the oil is incorporated and the mayonnaise is thick and creamy, whisk in the lemon juice or vinegar, salt, and white pepper if using. Adjust seasonings to taste. Store in an airtight container in the refrigerator for up to a week.