In a bowl, whisk until slightly frothy and smooth the 2 egg yolks, mustard, salt, and acid of choice (lemon, red wine vinegar, or rice vinegar).
2 egg yolks, 1 teaspoon ground mustard, 1/8 teaspoon salt, 1/4 cup acid for of your choice
Begin to add the oil by dripping it in slowly. I like olive oil, but it definitely gives it a strong olive oil flavor. As you drip in the oil, continue to whisk.
1 to 1-1/2 cups olive oil
Once it starts to thicken you can add the oil a little faster. Whisk until all oil is incorporated. If it's too thick, add a little more acid (lemon juice). If too thin, add a little more oil.