Bring all ingredients to room temperature. This is very important, as it helps with the emulsion of the ingredients.
Add egg yolks, vinegar, dijon mustard, salt pepper and lemon juice to a wide mouth canning jar, or any tall jar that can fit an immersion blender. Place immersion blender in the jar, atop the ingredients. Pulse to combine.
Slowly drizzle the oil, bit by bit, until it is about half combined, and your mixture is emulsified. At this point, you can add the rest of the oil in a quicker fashion, moving the blender up and down to combine.