Add egg, lemon juice, mustard, salt, and vinegar into a wide-mouth jar; ingredients should settle at the bottom.
Pour the avocado oil gently on top, allowing it to sit above the egg mixture without mixing.
Insert the immersion blender to the bottom of the jar, fully covering the egg mixture.
Turn on the blender and keep it still for about 10–15 seconds until the bottom turns thick and pale.
Slowly lift the blender upward as the mixture emulsifies, creating a creamy texture throughout.
Continue blending until all oil is incorporated and the mayonnaise is thick and smooth.
Taste and adjust salt or lemon juice if needed for balance.
Transfer to a sealed container and refrigerate immediately.