In a tall and narrow container, add the two eggs and ¼ cup of the avocado oil.
Place the immersion blender in the container, ensuring the blades are fully submerged in the mixture at the bottom. Start blending on a low speed to incorporate the ingredients without splashing.
With the immersion blender running, slowly start to drizzle the oil into the container. It’s crucial to start very slowly to begin forming the emulsion.
Continue blending, moving the immersion blender up and down slowly to incorporate more air and oil into the emulsion. You should see the mixture starting to thicken and form into mayonnaise.
Once all the oil is incorporated and the mayonnaise has formed, add the salt, pepper, ground mustard and fresh lemon juice. Blend briefly to mix thoroughly.
Taste your mayonnaise and adjust the seasoning if necessary, adding more salt or lemon juice as needed.
Transfer the mayonnaise to a clean jar or container with a lid. Store it in the refrigerator and use it within one week for the best freshness and safety.