Preheat your oven to 400°F (200°C). Pat the chicken thighs completely dry with paper towels and season them all over with salt and pepper.
Heat the olive oil in a large, oven-safe skillet over medium-high heat. Once the oil shimmers, place the chicken skin-side down in the skillet. Sear without moving for 6-8 minutes, until the skin is deep golden brown and crisp.
Flip the chicken and cook for 1 minute more. Transfer the chicken to a clean plate, leaving the rendered fat in the skillet.
Reduce the heat to medium. Add the chopped shallots to the skillet and cook, stirring occasionally, until they have softened, about 3 minutes.
Pour in the white wine to deglaze the pan. Use a wooden spoon to scrape up any browned bits from the bottom. Let the wine simmer until it has mostly evaporated, about 3 minutes.
Stir in the chicken broth and the whole-grain mustard. Bring the sauce to a gentle simmer.
Return the chicken to the skillet, placing it skin-side up. Transfer the skillet to the preheated oven. Bake uncovered for 15-20 minutes, or until the chicken is cooked through. An instant-read thermometer inserted into the thickest part of the thigh, avoiding bone, should register 165°F (74°C).
Carefully remove the chicken to a serving platter. Place the skillet back on the stovetop over medium heat. Whisk in the smooth Dijon mustard and the heavy cream.
Let the sauce simmer for 2 minutes to combine and slightly thicken. Taste the sauce and season with more salt and pepper if needed. Pour the sauce around the chicken on the platter and garnish with fresh parsley, if using.