Preheat the oven to 375ºF.
Add the corn flakes, garlic powder, dried thyme, paprika, salt, and flour to a large gallon bag and carefully crush all of the ingredients together with your hands. Do not crush all of the corn flakes into powder, there should be some larger chunks of corn flake. Set aside.
Crack 3 eggs in a large mixing bowl and whisk the eggs together. Dredge the chicken thighs through the egg and then through the cornflake mixture (you can keep the mixture in the bag). Be sure the chicken is fully coated in the cornflake mixture and set it on a plate. Repeat until all of the chicken thighs are coated.
Heat a large oven-safe skillet with sides (preferably cast iron) over medium/high heat and add olive oil. When the olive oil is fragrant, sear the chicken thighs for about 3 minutes or until the first side is golden brown. Be sure to gently move the thighs while they are searing to be sure they are not sticking to the skillet. Use a spatula to gently, but swiftly, flip the chicken over. Be sure not to separate the breading from the chicken. Sear the second side for 2 minutes and then remove the chicken from the pan.
Deglaze the skillet with ½ cup of broth and then add 1 tablespoon of olive oil. Add the onion to the skillet and season with ¼ teaspoon of salt. Sauté the onion for 3-4 minutes and then add the mushrooms and sauté for another 3 minutes.
Add the garlic, celery, and butter to the pan and mix everything together and let everything cook for another 3-4 minutes or until the butter is melted and begins to thicken. Pour the vegetable medley into the pan and toss and then add flour to the skillet and toss until all of the ingredients are coated in flour.
Next, add the rice, the rest of the salt, and the rest of the broth to the skillet and mix. Slowly add in the heavy cream, stirring constantly. Tie the fresh thyme and rosemary together with cooking twine and submerge it in the liquid. Finally, place the cooked chicken thighs on top of the whole mixture and cover.
Bake the skillet, covered, for 35 minutes, and then uncover the skillet and turn the heat to 450ºF and let it cook for another 5-10 minutes or until the chicken is golden brown. When the chicken is brown and the internal temperature is 165ºF, remove the skillet from the oven.*
Let the whole casserole sit for 10 minutes before serving.