Pat chicken dry and season with paprika, pepper and 1/2 teaspoon salt. Heat oil in a 5-quart Dutch oven over medium-high heat and brown chicken on one side for 5 minutes; transfer it to a plate while still partly raw.
Lower the heat to medium, add onion and carrot and cook for 4 minutes. Stir in garlic for 30 seconds, then rice and remaining salt for 1 minute.
Pour in broth and scrape up the browned bits. Bring to a simmer and nestle chicken browned-side up on the rice, adding its plate juices.
Cover tightly, reduce to low and cook for 18 minutes without stirring. Scatter frozen peas around the chicken, cover and cook for 5 to 7 minutes more until rice is tender and the thickest thigh reaches 165°F.
Remove the pot from the heat and rest covered for 5 minutes. Fluff rice gently around the thighs and serve 1 thigh with one-quarter of the rice and vegetables per portion.