Steak Tartare:
Mix all the ingredients together - do it just before serving!
Season the tartare with what you think is needed, then divide the mixture into 4 equal portions and shape them into patties.
Place each patty in the center of a large, flat plate.
Potato Chips:
Peel the potatoes and slice them into paper-thin slices using a mandoline.
Place them in cold water for about 30 minutes, changing the water once or twice during this period.
Boil the potato slices in a pot with water and a bit of vinegar. Let them boil for 2 minutes.
Place the potato slices on kitchen towels and dry them thoroughly. It's important that they are completely dry before frying them.
Heat the oil in a large pot, preferably a deep fryer, until it reaches 170 degrees Celsius (338 degrees Fahrenheit).
Fry the potato slices in the oil for a couple of minutes (do not crowd the pot as this lowers the oil temperature).
Let the potato slices drain on a kitchen towel.
Herb Mayonnaise:
Start by making a herb oil:
Rinse the tarragon and remove the thickest stems.
Peel the garlic clove and cut it in half.
Blend all the ingredients for the tarragon oil in a blender or mini chopper.
Strain the oil and set it aside.
Now, make the mayonnaise:
Take all the ingredients out of the fridge and let them come to room temperature before you start. This is important, as having a uniform temperature is key to a good mayonnaise that doesn't separate.
Whisk the egg yolks and Dijon mustard until light yellow.
Add your homemade tarragon oil in a thin stream while continuing to whisk.
You will now see the mayonnaise becoming thicker and thicker. When you think it has the right consistency, stop whisking.
Add white wine vinegar, lemon juice, salt, and pepper, and season the mayonnaise to taste.
Serving:
Arrange the chips on the plates with the tartare.
Place drops of tarragon mayonnaise around the plates. Serve the rest of the mayo in a bowl on the side.
This dish is best enjoyed with a mixed green salad with an oil-vinegar dressing.