Season chicken on both sides with salt and pepper. Heat half of the olive oil in a large heavy skillet over medium heat. Add the chicken and cook until well browned, about 3 minutes per side. Transfer to a plate and cover or tent with foil.
Add the remaining olive oil to pan. Add shallots; cook, stirring, until softened, 2 to 3 minutes. Add broth and wine and bring to a medium simmer. Cook until reduced by half, about 3 minutes.
Return the chicken and any accumulated juices to the pan; reduce heat to low. Simmer until the chicken is cooked through, about 3-4 minutes. Transfer the chicken to a warmed platter. Stir mustard, sour cream, nutmeg and tarragon into sauce. Warm through. Season to taste with salt and pepper and spoon over the chicken. Garnish chicken thighs with fresh tarragon sprig.