Add the egg, lemon juice, honey, salt, dijon mustard, and white vinegar to a tall jar or container suitable for an immersion blender.
Pour the olive oil on top. Let everything settle for a few seconds.
Place the immersion blender at the bottom of the jar and blend on low speed without moving it for about 20 seconds, until the mixture starts to emulsify.
Once it begins to thicken, slowly lift the blender to incorporate the remaining oil until smooth and creamy.
Taste and adjust seasoning if needed. Store in an airtight container in the refrigerator for up to 1 week.