Place a rack in middle of oven; preheat to 400°. Generously season 4 chicken legs (thigh and drumstick; about 2 lb. total), patted dry, with kosher salt and freshly ground pepper. Set aside.

Whisk together 8 garlic cloves, finely grated, ⅔ cup apricot jam, ¼ cup Dijon mustard, ¼ cup soy sauce, 2 Tbsp. extra-virgin olive oil, 2 Tbsp. unseasoned rice vinegar, and 1 tsp. freshly ground pepper in a large bowl. Set dressing aside.

Place 1½ lb. small carrots (about 14), peeled, sliced into 2" pieces, halved if very large, and 1 large red onion, halved, thickly sliced, on a rimmed baking sheet. Sprinkle with 2 tsp. Diamond Crystal or 1¼ tsp. Morton kosher salt and drizzle ¾ cup reserved dressing over; toss to evenly coat. Scatter vegetables out in a single layer.

Place reserved chicken legs in remaining dressing and toss to coat; arrange on top of vegetables. Spoon any remaining dressing in bowl over chicken, allowing it to drip down onto baking sheet. Roast, rotating baking sheet halfway through, until carrots are tender, chicken is deep golden brown, and an instant-read thermometer inserted into the thickest part of a leg registers 165°, 40–50 minutes.

Move chicken to edges of baking dish and toss vegetables in any sauce pooled on baking sheet. Using a slotted spoon, transfer vegetables to a platter, allowing any excess liquid to drip back onto baking sheet. Arrange chicken on top; discard any excess liquid on baking sheet. Scatter thinly sliced chives over chicken and vegetables if desired.