Coarsely chop Walnut (1 cup) and toast them lightly in a dry skillet. Set aside to cool.
Cut stems from Brussels Sprouts (1 pound). Thinly slice brussels sprouts starting at the rounded end, working your way toward the core or stem. Once you start getting to the hard stem, stop slicing. You just want to use the leafiest part of the sprout. Sift through sliced sprouts with your fingers, breaking them up into little ribbons and removing any bits of core.
In a small food processor or separate bowl with a lid, combine White Balsamic Vinegar (1/3 cup), Olive Oil (1/4 cup), Tarragon (2 tablespoon), Kosher Salt (to taste), and Freshly Ground Black Pepper (to taste). Blend or shake vigorously to emulsify ingredients.
Combine sprouts, Mâche (3 ounce), Iberico Cheese (3/4 cup) and walnuts in a large bowl. Gradually mix dressing into the salad, your clean hands work as the best kitchen tool for this task, and serve.