Salt chicken all over. Loosely cover with plastic. Refrigerate up to 3 days or at least a few hours if time permits.
Take chicken out one hour prior to cooking to take chill off.
Pat dry. If you are not avoiding grains, pat dry with flour. I didn't use the flour.
Using a stainless frying pan or a cast iron pan, get pan hot. Pan needs to be large enough to give room to chicken thighs so they fry and not steam. You may need to do this in batches.
Once pan is hot, add oil. Lower heat, place chicken in pan and and cook without moving (if you move chicken, skin will stick). Fry for ten minutes until you can easily turn over. Once you turn over, cook another 2-3 minutes.
Remove chicken to a plate. Use a stainless pan for adding wine, not cast iron. You can scrap any bits into the new pan.
Add wine, shallots, mustard and stir. Heat for five minutes.
Add chicken thighs back in and braise for 25 minutes skin side up, no lid. Add in thyme sprigs.
Season with salt and pepper.