Preheat the oven to 400°F. Pat the chicken thighs dry with paper towels, then season both sides with salt, black pepper, and smoked paprika.
Whisk together the Dijon mustard, yellow mustard, honey, minced garlic, and chicken broth in a small bowl until smooth. Set the sauce aside.
Heat the olive oil in a large oven-safe skillet over medium-high heat. Place the chicken thighs in the skillet skin-side down and cook for 5–7 minutes, or until the skin is deeply golden and releases easily from the skillet.
Flip the chicken thighs and cook for another 1–2 minutes. Transfer them to a plate, leaving the rendered fat and browned bits in the skillet.
Add the halved potatoes to the skillet and cook for 4–5 minutes, turning occasionally, until lightly browned. Place as many potatoes cut-side down as possible for better color.
Pour the honey mustard sauce over the potatoes and stir to coat. Nestle the chicken thighs back into the skillet with the skin facing upward.
Transfer the skillet to the oven and roast for 20–25 minutes, or until the chicken reaches an internal temperature of at least 165°F and the potatoes are fork-tender.
Remove the skillet from the oven. Stir in the butter, if using, and let the chicken rest for 5 minutes. Garnish with chopped parsley and serve with the potatoes and honey mustard pan sauce.