Sear the chicken Warm the olive oil in a large pot over medium-high heat. Season the chicken with salt and pepper, then place it skin-side down. Sear for about 3–4 minutes per side, until golden. Remove and set aside.
Sauté onion and garlic Reduce heat to medium. Add the diced onion and cook until softened, about 3–4 minutes. Stir in the garlic and cook for another minute.
Add rice and broth Pour in the rice, chicken broth, thyme, salt, and black pepper. Stir well, scraping up any browned bits from the bottom of the pot.
Return chicken to the pot Nestle the chicken pieces on top of the rice. If using vegetables, add them now, either stirred into the rice or placed around the chicken.
Cook Bring the mixture to a gentle boil, then reduce the heat to low. Cover and simmer for 20–25 minutes, or until the rice is tender and the chicken is cooked through.
Rest and serve Remove from heat and let the dish rest, covered, for a few minutes. Serve hot and enjoy.