Combine egg, lemon juice, and mustard in food processor and blend until frothy.
Using the drip hole in the top of the processor, or pouring teaspoon by teaspoon to start, drizzle the oil in drop by drop. **Do not rush this process or you will end up with scrambled eggs mixed with oil!**
Once you have quite a few drops in there, you can pour the oil into the feed tube part of the food processor to let that useful drop hole control the rate of flow for you.
Refrigerate in sealed container. This will keep for a week or so.