Prep the basics. Cut the chicken into bite-size pieces and pat dry. Season with salt, pepper, paprika, and thyme.
Rinse the rice until the water runs mostly clear. Chop the onion, mince the garlic, and cut broccoli into small florets.
Brown the chicken. Heat oil in a large, deep skillet or Dutch oven over medium-high heat. Add the chicken in a single layer and cook 4–6 minutes, turning once, until browned and mostly cooked through.
Transfer to a plate.
Build the flavor base. Lower heat to medium. Add onion and a pinch of salt to the same pan. Cook 3–4 minutes, stirring and scraping up brown bits.
Add garlic and red pepper flakes; cook 30 seconds until fragrant.
Toast the rice. Stir in the rinsed, drained rice. Cook 1–2 minutes to lightly toast and coat with oil and aromatics. This helps the rice stay fluffy and flavorful.
Add liquid and simmer. Pour in the chicken broth and bring to a gentle simmer.
Taste the liquid and adjust seasoning with salt and pepper. Return the chicken and any juices to the pan, nestling it into the rice.
Cover and cook. Reduce heat to low, cover tightly, and cook for 10 minutes. Try not to lift the lid; you want to trap steam so the rice cooks evenly.
Add broccoli. After 10 minutes, quickly lift the lid, scatter the broccoli on top, and cover again.
Cook another 8–10 minutes, until the rice is tender, liquid is absorbed, and broccoli is crisp-tender.
Finish and fluff. Remove from heat and rest, covered, for 5 minutes. Add butter and Parmesan or cream if using. Fluff gently with a fork to mix broccoli and chicken through the rice.
Serve. Squeeze lemon over the top for brightness and taste for final seasoning.
Add more pepper or a pinch of salt if needed.