3/4 cup olive or vegetable oil (or a combination), divided
1 teaspoon white-wine vinegar or cider vinegar
1 1/2 teaspoons fresh lemon juice
1/4 teaspoon white pepper
Whisk together yolk, mustard, and 1/4 teaspoon salt until combined well. Add about 1/4 cup oil drop by drop, whisking constantly until mixture begins to thicken. Whisk in vinegar and lemon juice, then add remaining 1/2 cup oil in a very slow, thin stream, whisking constantly until well blended. If at any time it appears that oil is not being incorporated, stop adding oil and whisk mixture vigorously until smooth, then continue adding oil. Whisk in salt to taste and white pepper. Chill, surface covered with plastic wrap, until ready to use.