In a 6 to 8-quart crock pot, combine the barley, mushrooms, chicken, chicken broth, lemon juice, white wine, garlic, thyme, salt, onion powder, red-pepper flakes and several generous grinds of black pepper.
Stir to combine; cook, on high, for 3 hours.
At first, it will seem like there is too much liquid, but the dish will thicken as it cools and as you stir.
Stir in the frozen peas and let them heat through; about 2 minutes.
In a small bowl, stir together the crème fraîche and mustard; fold it into the barley mixture.
The chicken thighs should be falling apart; using a spatula, break them into coarse chunks.
Taste and add more mustard for a stronger flavor, if desired.
Stir in the chopped tarragon or dill and serve.
Pass parmesan cheese at the table for topping.
