Place a rack in highest position in oven; preheat to 450°. Place panko in a small bowl. Mash butter, mustard, and thyme leaves in another small bowl with a fork (it will be a little lumpy). Season chicken thighs on both sides with salt and pepper. Arrange skin side up a rimmed baking sheet and smear all over skin side of thighs. Working with 1 piece at a time, firmly press chicken, skin side down, into panko so crumbs adhere. Place back on baking sheet skin side up. Arrange carrots and thyme sprigs around chicken and drizzle with oil; season with salt and pepper. Toss to coat and bake until carrots are tender and chicken is cooked though, 25–30 minutes. Heat broiler. Broil chicken and carrots just until panko is golden brown and carrots are tender and browned in spots, about 2 minutes. Transfer to a platter and pour pan juices over top.