Find a pot. Put the potatoes in it and add cold water so that the potatoes are covered.
Boil the potatoes for 15 minutes. Drain the water and let the potatoes cool down.
While the potatoes cool, find an immersion blender and a tall glass that fits it.
Crack the egg into the glass.
Add the salt to the glass followed by white wine vinegar and Dijon mustard.
Add the oil in a steady stream.
Place the immersion blender all the way to the bottom of the glass and turn it on.
Move the immersion blender in a circular motion at the bottom of the glass for a few seconds.
Slowly lift the immersion blender while continuing the circular motion. Continue until you reach the top of the glass and the mayo has thickened.
Add tarragon, bearnaise essence, and lemon juice and mix it with the mayo. Peel the skin off the cooled potatoes and cut them into smaller pieces.
Fold the potatoes into the bearnaise mayo.
Place the potato salad in the fridge for at least 30 minutes - preferably 2 hours.
Serve the cold bearnaise potato salad.