Preheat oven to 350 degrees F.
Heat olive oil in a large saucepan or skillet that has a lid (set the lid aside for now).
Line a baking sheet with foil and place carrots on the foil. Toss with olive oil and season with salt and pepper. Bake the carrots for 20 - 25 minutes, turning and mixing them every 5 - 10 minutes so they brown evenly.
Meanwhile, place chicken “pretty side” down in hot skillet, sprinkle with salt and pepper, and sauté for 5 - 8 minutes, until browned on one side. Flip chicken and cook until brown on the other side, then add 1 cup of the chicken stock/broth to the pan. Reduce the heat to medium-low and place the lid on the pan to allow the chicken to cook through. The stock will begin to reduce.
When chicken is cooked thoroughly (registers at least 165 degrees F with an instant-read thermometer/Thermapen), remove to a plate and set in a warm place (I put mine in the microwave NOT turned on!).
Add thyme, garlic, and remaining 1/2 cup chicken stock/broth to pan sauce, turning heat to high. Cook uncovered for about 5 minutes, or until the liquid thickens into a gravy.
Add the cooked chicken thighs back to the pan with the sauce. Spoon sauce over the chicken.
To serve, pour sauce over both chicken and carrots. Sprinkle extra fresh thyme if desired.