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Place chicken thighs in a large bowl with sliced onion, 2 T thyme, chiles, bay leaves, and 1/4C vermouth. Using your hands, toss to coat the chicken well. Cover and refrigerate at least 4 hours, preferably overnight. Place the breadcrumbs in a med bowl. Heat large saute pan over med heat for 1 minute. Add 3 T butter, and cook until it's brown and smells nutty. Use a rubber spatula to scrape brown butter over the breadcrumbs. Wait 1 min, and then toss w/ parsley and 1 T thyme. Preheat the oven to 375u00b0F.Return the saute pan to med heat for 1 min. Swirl in the remaining 1T butter, and when it foams, add shallots and remaining 1 t thyme. Saute about 2 mins, until shallots are translucent. Add remaining 1/2 cup vermouth and reduce by half. Transfer to a bowl and let cool a few mins. Whisk in the mustard, egg, chopped tarragon, and a pinch of black pepper. Bring chicken to room temperature. Discard seasonings, and pat dry with paper towels. After 15 mins, season the thighs well on both sides with salt and pepper. Return the same saute pan to high heat for about 2 mins. Swirl in olive oil, and wait 1 min. Place chicken thighs in the pan, skin side down, and cook 8 to 10 mins, until the skin is a deep golden brown. Turn the thighs over and cook a minute or two on the other side. Place chicken on the leeks. Turn off heat and discard the fat. Add chicken stock to the pan, and scrape to release the crispy bits. Pour the chicken stock over the braised leeks. Toss the chicken thighs in the bowl with the mustard mixture, slathering them completely, and then rearrange them over the braised leeks. Spoon any remaining mustard mixture over the chicken thighs. Top each thigh with breadcrumbs, patting with your hands to make sure they get nicely coated. (You want lots of mustard mixture and lots of breadcrumbs.) Bake about 40 mins, until the chicken is just cooked through. Turn the oven up to 475u00b0F and cook the chicken thighs another 10 mins, until the breadcrumbs are golden brown.
