1.
Pat chicken dry with paper towels and season with sea salt and pepper.
Heat oil in a 12-inch skillet over medium-high heat until just smoking. Brown chicken well on both sides, about 8 minutes total; transfer to a plate.
2.
Add mushrooms, onion, and wine to fat left in skillet and cook over medium heat until liquid has evaporated and mushrooms are browned, 8 to 10 minutes.
Stir in garlic and cook for 1 minute. Slowly whisk in broth, scraping up any browned bits, and bring to boil. Return browned chicken and any accumulated juices to skillet.
Reduce heat to medium-low, cover, and cook until chicken registers 160° F (71° C), about 10 minutes.
3.
Transfer chicken to a serving platter and tent loosely with aluminum foil.
Whisk 0.5 cup of the sauce and the tapioca flour into the cheese in a bowl to temper, then stir the cheese mixture back into the pan.
Stir in lemon juice, tarragon, and nutmeg and return sauce to a brief simmer.
Season with sea salt and pepper to taste and pour over chicken.
Serve.