Prep the chicken. Pat the chicken dry with paper towels. Toss with salt, pepper, paprika, and thyme.
This helps build flavor and a light crust.
Heat the pan. Place a large, deep skillet over medium-high heat. Add olive oil and 1 tablespoon of butter. When shimmering, add the chicken in a single layer.
Brown the chicken. Cook 4–6 minutes, stirring once or twice, until lightly golden and mostly cooked through.
Transfer to a plate; it will finish cooking later.
Soften the aromatics. Lower heat to medium. Add another tablespoon of butter, onion, and a pinch of salt. Cook 2–3 minutes until translucent.
Stir in the garlic and cook 30–60 seconds until fragrant—don’t let it brown.
Toast the rice. Add the uncooked rice to the skillet. Stir for 1–2 minutes so the grains get glossy and lightly toasted in the garlic butter.
Deglaze and simmer. Pour in the chicken broth and scrape the pan to release browned bits. Bring to a gentle simmer.
Add the chicken back. Return the chicken and any juices to the skillet.
Stir, then reduce heat to low, cover, and cook for 15 minutes without lifting the lid.
Finish the rice. After 15 minutes, check the rice. If most liquid is absorbed and rice is nearly tender, stir in the peas and the remaining tablespoon of butter. If using, add milk or cream now.
Steam and rest. Cover and cook 3–5 minutes more, then turn off the heat and let it rest, covered, for another 5 minutes.
This final rest finishes the rice and keeps it fluffy.
Taste and brighten. Fluff with a fork. Adjust salt and pepper. Stir in parsley and a squeeze of lemon for a clean, fresh finish.
Serve warm. Spoon into bowls.
Add extra lemon on the side if you like a little zip.