Add the egg, vinegar, mustard, and oil to a tall jar, in that order, so the egg sits at the bottom.
Insert an immersion blender all the way to the bottom of the jar. Without moving it, blend on high for 10–15 seconds until the emulsion starts to form and turn opaque at the base.
Once it's holding together, slowly tilt and lift the blender through the rest of the mixture, blending until fully combined, smooth, and thick.
Season to taste and transfer to an airtight jar. Refrigerate until ready to use.
Chef's Tips
Use a fresh egg, ideally at room temperature — freshness matters more here since it stays raw, and a fresher egg emulsifies more reliably too.Keep the immersion blender flat on the bottom of the jar and don't move it for the first several seconds — this lets the emulsion form at the base first, then slowly lift and tilt it through the rest of the oil once it's started to thicken.Add the egg, vinegar and mustard to the jar before the oil, as written — mustard acts as a natural emulsifier, and having it in contact with the egg first helps the mixture come together and stay stable.
Storage & Reheating
Refrigerate for up to 4 days in an airtight jar or container. Freezing isn't recommended, since the raw-egg emulsion will split once thawed. No reheating required — this one's served cold.