Place the room-temperature egg in the bowl of a food processor and blend for about 20 seconds to break it down.
Add the dijon mustard, salt, and grate the garlic cloves directly into the food processor. Blend again for another 20-30 seconds until well combined.
With the processor running, very slowly drizzle in the vegetable oil in a thin stream.*** Continue blending until the mixture turns pale, thick, and creamy-about 30 seconds after the oil is fully incorporated.
Add the lemon juice and honey, then blend briefly to combine. Taste and adjust salt or lemon juice as needed.
Transfer to a clean airtight container and refrigerate.**** Use within 4 days for best quality.
*Room-temperature ingredients are important for a smooth, stable emulsion. If needed, place the whole egg in a bowl of warm (not hot!) water for a few minutes before starting. Since this recipe uses raw egg, I highly recommend using a pasteurized egg. Pasteurized eggs are gently heat-treated to reduce the risk of harmful bacteria without cooking the egg, which makes them a better choice for uncooked sauces like this one.**Use a neutral oil, such as vegetable, canola, or avocado oil, for the smoothest flavor. I don’t recommend extra virgin olive oil for this food processor method because it can turn bitter when blended at high speed.***Add the oil slowly while blending to prevent the aioli from breaking. Once the emulsion starts forming, you can drizzle slightly faster.****For a stronger garlic flavor, refrigerate the sauce for 30 minutes before serving.