Prepare your veggies by chopping the onions and carrots and mincing the garlic. Pat the chicken quarters with paper towel to remove any excess humidity.
Heat up the skillet oven medium-high heat. Drizzle the olive oil in the pan and only cook 2 chicken quarters at a time. Over crowding the pan will create too much steam and will prevent the chicken from crisping up. The chicken does not need to cook through at the this time. Once the chicken is nice and golden on both sides, place on a clean plate and reserve.
Place the diced carrots and onion in the same skillet. Cook for 2-3 minutes. Add in the minced garlic and the salt and cook for another 2 minutes.
Deglaze the pan by slowly pouring in the chicken broth. Use a wooden spoon to scrape up all the delicious, stuck on bits from the bottom.
Add tarragon to the pan and stir in the Dijon mustard. Proceed with pouring in uncooked rice in the skillet, making sure that it is evenly distributed.
Place the chicken quarters back into the skillet. Place the lid on the skillet and carefully place it in the preheated 350F oven. Bake for 45 minutes. After that time, remove the lid from the skillet and bake for an additional 10 minutes to crisp everything up. Remove from the oven and enjoy!
Video
Notes
GREASE SPLATTERS: I recommend using a Stainless Grease Splatter Screen for the skillet when cooking the chicken. It will prevent grease burns and let the chicken crisp up nicely.