One day ahead, combine the chicken thighs with mustard, wine, salt, and pepper in a mixing bowl. Massage well with your hands, cover, and refrigerate.
An hour before cooking, take the bowl containing the chicken and its marinade from the refrigerator and allow it to come to room temperature. When you’re ready to cook the dish, remove the chicken thighs from the bowl and wipe dry with paper towels.
Heat a heavy-bottomed sauté pan over medium heat. Add the olive oil and butter. Once the butter foams, add the chicken thighs skin side down and cook for 8 to 10 minutes, until the skin is golden and crisp. Flip thighs over and continue to cook for 2 minutes.
Remove the chicken to a platter, leaving the remaining renderings in the pan. Next, add the shallots, garlic, bay leaves, and thyme to the pan and sauté for about 5 minutes, until soft but not brown. If you need to lower the heat to accomplish this, now is the time.
Next, raise the heat to high and add the wine, deglazing any of the flavorful bits from the bottom of the pan as the wine come to a boil. Once the wine has reduced by about ¾, add the chicken stock. Return to the boil and reduce by ⅓.
Once the stock has reduced, add the chicken thighs back into the pan skin side up, cover, and reduce the heat to accomplish a very gentle simmer. Cook chicken for 20 minutes, then turn off the heat and allow to rest, covered.
To finish, remove the chicken from the pan to the platter and stir in the cream, mustard, and tarragon. Simmer over medium heat for about 10 minutes, until the sauce thickens slightly. Taste and season with salt and pepper, then return the chicken to the pan, swirl the contents, and serve.