Season the chicken thighs generously with salt and pepper. Heat 2 tablespoons of olive oil in a heavy cast iron skillet over medium-high heat. Sear the chicken thighs on both sides until they achieve a golden-brown crust, approximately 3-4 minutes per side. Once seared, remove the chicken from the skillet and set aside.
Add the remaining tablespoon of olive oil to the skillet. Sauté the diced onion until it becomes translucent, about 3-4 minutes. Stir in the minced garlic and cook until fragrant, roughly 30 seconds. Introduce the diced yellow and red bell peppers, sliced carrot, mushrooms, and herbs. Cook the mixture for about 5 minutes, allowing the vegetables to soften slightly.
Pour the red wine into the skillet, using a wooden spoon to scrape up any browned bits from the bottom. Let the wine reduce for about 2 minutes. Add the crushed tomatoes, tomato paste, halved Roma tomatoes, and red pepper flakes. Season with additional salt and pepper according to your taste. Return the seared chicken thighs to the skillet, nestling them into the sauce.