In a large mouth mason jar, combine eggs, anchovies, garlic, salt, pepper, vinegar, and lemon juice. Using an immersion blender, blend until completely smooth. About 30 seconds.
With the blender on, slowly pour in olive oil and move blender up and down in the jar until all oil is added and mixture is thick.
Notes
*Use 2 tablespoons of garlic oil in place of the garlic to keep it low FODMAP