Place the safflower oil in mason jar just wide enough to fit an immersion blender.
Drop an egg into the jar.
Once settled, take immersion blender and place all the way down to the bottom of the jar, placing blade over egg yolk.
Turn immersion blender on high and hold for about 10 seconds, then lowly raise up and down throughout mixture until oil emulsifies, roughy 30 seconds.
Add garlic, lemon juice, white wine vinegar, salt and pepper. Blend until combined and smooth.
Stir in the chopped tarragon. Set aside or refrigerate until ready to use.