Step 1

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.

Step 2

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.

Step 3

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.