Preheat the oven to 375°F (190°C) and lightly grease a large oven-safe skillet or baking dish.
Pat the chicken breasts dry and gently pound very thick pieces to an even thickness.
Combine the garlic powder, paprika, Italian seasoning, salt, and black pepper, then season both sides of the chicken evenly.
Heat olive oil in an oven-safe skillet over medium-high heat and brown the chicken for 2–3 minutes per side, then transfer it to a plate.
Add the diced onion and carrots to the same skillet and cook for 4–5 minutes until the onion begins to soften.
Stir in the minced garlic and cook for about 30 seconds until fragrant.
Add the uncooked rice and stir with the vegetables for 1–2 minutes to lightly toast the grains.
Pour in the chicken broth and add butter, thyme, salt, and black pepper, scraping up the browned bits from the bottom of the skillet.
Place the browned chicken on top of the rice mixture and cover the skillet tightly with an oven-safe lid or aluminum foil.
Bake for 25–30 minutes, then check that the chicken reaches 165°F (74°C) and the rice is tender.
Stir the frozen peas into the cooked rice during the final few minutes so they warm through without becoming mushy.
Let the dish rest, covered, for 5–10 minutes, then fluff the rice gently with a fork and adjust the seasoning.
Slice the chicken or serve the breasts whole over the rice and vegetables, spooning the flavorful rice onto each plate.