Pat the chicken dry and season both sides with 1 1/4 tsp kosher salt and 3/4 tsp freshly ground black pepper. Drying the surface removes moisture so the thighs will brown rather than steam — browning builds deep flavor through Maillard reaction.

Heat a wide, heavy skillet or sauté pan (cast-iron or stainless steel) over medium-high heat. Add 2 tbsp olive oil and let it shimmer but not smoke. A hot pan ensures a quick sear that seals flavor; waiting until the oil is hot prevents sticking.

Add chicken thighs in a single layer (work in two batches if necessary). Sear without moving for 3–4 minutes per side until a deep golden-brown crust forms. Don't overcrowd the pan — overcrowding lowers the pan temperature and causes steaming instead of browning.

Transfer the seared thighs to a plate and tent loosely with foil. Leave any rendered fat and browned bits (fond) in the pan — those bits hold concentrated flavor and will enrich the sauce.

Lower heat to medium and add the thinly sliced onion. Cook for 6–8 minutes, stirring occasionally, until soft and beginning to caramelize; this develops natural sweetness that complements the tomatoes. If the pan looks dry, add a splash (1–2 tbsp) of stock to deglaze and lift browned bits.

Add the minced garlic, 1 tsp dried oregano, and 1/2 tsp red pepper flakes (if using). Sauté for 30–60 seconds until fragrant — garlic burns quickly, so keep it moving for a brief toast to release aroma without bitterness.

Pour in the 400 g crushed tomatoes and 120 ml chicken stock; stir to combine and scrape up any fond on the bottom of the pan. The stock thins the tomatoes slightly so they simmer evenly and the fond dissolves, adding complexity to the sauce.

Bring the sauce to a gentle simmer, then return the browned chicken thighs (and any accumulated juices) to the pan, nestling them into the sauce skinless-side up. Add the halved Kalamata olives and rinsed capers. Tucking the chicken into the sauce ensures even cooking and allows the meat to absorb the tomato-olive flavors.

Reduce heat to low, partially cover the pan, and simmer gently for 25–30 minutes, turning thighs once midway. A gentle simmer (not a rolling boil) keeps the chicken tender; slow, moist heat breaks down connective tissue for a silky texture.

Five minutes before the end of cooking, add the roasted carrots to warm through and release their caramelized sweetness. Taste the sauce and adjust seasoning with the remaining 1/4 tsp salt and additional black pepper if desired. Adding carrots near the end preserves their texture and concentrated roasted flavor.

If the sauce is too thin, remove the chicken and boil the sauce briskly for 2–3 minutes to concentrate; if too thick, stir in a splash of stock. Finish by stirring in chopped parsley and a quick drizzle of extra-virgin olive oil for gloss and brightness; a squeeze of lemon (optional) will lift the whole dish.

Serve the braised thighs spooned over creamy polenta, mashed potatoes, buttered pasta, or with crusty bread to soak up the sauce. Garnish with additional parsley and a few whole olives for presentation.