1. Heat oven to 375°. Heat oil in a large saucepan or Dutch oven over medium-high heat. Season chicken with salt and pepper. Brown both sides of chicken, flipping once, about 10 minutes; cook in batches to avoid crowding the pan or it will not brown well. Transfer chicken to a plate and set aside. Add the shallots and garlic to pan, cook, stirring occasionally, until shallots are golden, 3-5 minutes. Add the wine, stock, mustard, and thyme, and bring to a boil. Return the chicken to the pan with any juices, cover with a lid, and transfer to the oven. Bake until chicken is cooked through, about 45 minutes, or until an instant-read thermometer inserted into the thickest part of the thigh reads 165°. Alternatively, you can cook it on the stovetop over a very low heat (a bare simmer).
2. Transfer chicken to a serving platter and keep warm. Return saucepan to stove; bring to a boil. Cook, stirring occasionally, until reduced by half, 8-10 minutes. Spoon sauce over chicken; garnish with tarragon.