Heat the oven to 425°F (220°C). Line a rimmed sheet pan with parchment if desired. Cut the carrots into evenly sized sticks about 1/2 inch thick.
Toss the carrots with 1 tablespoon of the olive oil, half the kosher salt, and half the black pepper. Spread them on the pan and roast for 10 minutes.
Pat the chicken thighs dry. Rub them with the remaining olive oil, salt, and pepper. Move the carrots to make room and arrange the thighs skin-side up, leaving space between pieces.
Whisk the Dijon mustard, maple syrup, apple cider vinegar, garlic, and thyme in a small bowl.
Roast for 20 minutes, then brush the glaze over the chicken. Continue roasting for 12 to 20 minutes, until the thickest part of each thigh reaches 165°F (74°C) on an instant-read thermometer without touching bone and the carrots are tender. If the glaze darkens too quickly, loosely cover the chicken with foil.
Rest the chicken for 5 minutes before serving. Spoon any pan juices over the chicken and carrots.