Preheat oven to 375°F. Adjust oven racks so skillet will sit in center of oven.
In a medium bowl, whisk together ⅓ cup Dijon mustard, ⅓ cup maple syrup, 3 pressed or minced garlic cloves, 1 tablespoon apple cider vinegar, ¼ cup chicken broth, ½ teaspoon salt, ¼ teaspoon freshly ground black pepper, and 1 chopped shallot. Set aside.
Pat chicken thighs completely dry on all sides with paper towels. Liberally season chicken with sea salt and black pepper on both sides.
Heat large oven-safe skillet over medium-high heat. When pan is very hot, add 1 tablespoon oil and swirl pan to distribute oil evenly across pan surface. Continue heating pan until oil is hot and shimmery.
When oil is hot, place chicken thighs in skillet skin-side down. Sear chicken thighs 7 to 8 minutes or until skin is golden brown and releases easily from pan. If skin sticks to pan, continue searing until skin releases easily.
Flip chicken thighs over. Pour maple-dijon mixture into pan around chicken, avoiding pouring directly onto crispy chicken skin. Nestle 3 fresh rosemary sprigs around chicken. Place skillet in preheated oven.
Roast chicken thighs 15 to 17 minutes, or until internal temperature of chicken reaches 175° to 180°F. Note: Skillet will be very hot. Always use potholder when moving skillet or checking chicken temperature.
Once temperature is reached, carefully remove skillet from oven using potholder. Transfer chicken thighs to serving plate and set aside.
If desired, place skillet with sauce on burner and reduce over medium heat 3 to 5 minutes until desired consistency is reached.
After 5 minutes rest time for chicken thighs, serve over mashed potatoes, cauliflower mash, risotto, couscous, pasta, or rice. Spoon plenty of sauce over chicken and sides.