Preheat oven to 375 degrees F.
Season chicken thighs well with salt and pepper, to taste. Melt 2 tablespoons butter in a large oven-proof skillet over medium-high heat. Add chicken, skin-side down. Once it’s in the pan, don't move it for a few minutes, until the skin is golden brown and releases easily without tearing (about 5 minutes). Turn chicken over and sear the other side for 2-3 minutes. Remove chicken to a plate and set aside.
Pour out the fat from the pan, leaving one tablespoon and melt remaining 1 tablespoon butter in the skillet. Add mushrooms and leeks and cook until the mushrooms are lightly brown, about 5-7 minutes. Add the garlic and cook 1 minute more. Add wine and bring it to a simmer, then add the chicken broth and the herbs. Return chicken to the skillet.
Place into oven and roast until completely cooked through, reaching an internal temperature of 165 degrees F, about 20-25 minutes. Remove the chicken to a serving platter and cover with foil; To the mushrooms, stir in cream and mustard. Bring to a simmer and cook until slightly reduced, about 5 minutes. Turn off the heat and stir in the lemon juice.
To serve, keep the skin crispy by spooning the mushroom mixture on a plate and placing the chicken on top (if using skinless, just top with sauce).
*This recipe works well with boneless, skinless thighs as well but cut the baking time to 15-20 minutes.