Preheat oven to 350f. Also, heat bacon fat in cast iron skillet on medium.
Cut carrot into desired sizes. Coat in olive oil, salt, and pepper. Bake at 350f for 20-25 minutes while chicken cooks. Be sure to give the sheet a good shake every 5-10 minutes for even browning.
Place chicken “pretty side” down in hot skillet. Sprinkle with salt and pepper. Saute for 5-8 minutes, until browned on one side.
Once brown, flip chicken. Cook until brown. Once both sides of chicken are brown, pour 1 cup of stock in. Turn heat down just a click and place lid on pan and allow to cook through the chicken. Stock will begin to reduce.
Once stock is reduced to 1/4 inch or so at the bottom of your pan, place thyme and garlic in. Allow to cook for a 2 minutes.
Remove chicken from pan, but leave the liquids. Pour remaining 1/2 stock into skillet and crank the heat back up. Cook uncovered for 5 minutes or so, until liquids thicken into a gravy.
Pour gravy over chicken and carrots. Sprinkle a little more fresh thyme over and gobble it up!