Warm the olive oil in a large deep skillet over medium heat.
Season the chicken with salt, pepper, and paprika. Sear until lightly browned, 4–5 minutes. Transfer to a plate.
Melt butter in the same skillet. Soften the onion for 3–4 minutes.
Stir in garlic and thyme; cook until fragrant, about 30 seconds.
Toast the rice in the pan for 1 minute, stirring to coat.
Pour in the broth and scrape up any browned bits. Return the chicken and juices to the pan.
Bring to a gentle simmer. Cover and cook until rice is almost tender, 8–10 minutes.
Stir in the cream and the peas and carrots. Simmer uncovered until the rice is tender and sauce thickens, 3–4 minutes.
Remove from heat. Fold in Parmesan and lemon juice. Taste and adjust seasoning.
Rest 2 minutes to set. Sprinkle with parsley and serve warm.