Start the base: In a large pot or Dutch oven, heat butter and olive oil over medium heat. Add onion, carrots, and celery.
Cook, stirring occasionally, until softened and fragrant, about 6–8 minutes.
Add aromatics: Stir in garlic, thyme, parsley, bay leaf, and paprika. Cook for 30–60 seconds until the garlic is fragrant.
Make the roux: Sprinkle flour over the vegetables. Stir to coat and cook for 1–2 minutes.
This step thickens the soup and prevents a raw flour taste.
Add broth gradually: Pour in about 1 cup of broth while stirring to loosen the roux. Once smooth, add the remaining broth. Bring to a gentle boil.
Cook the rice: Add the rice.
Reduce heat to a simmer, cover partially, and cook for 15–18 minutes, stirring occasionally to prevent sticking. The rice should be tender but not mushy.
Stir in chicken: Add the shredded chicken and simmer for another 3–5 minutes to warm through.
Make it creamy: Lower the heat. Stir in the heavy cream and peas.
Simmer gently for 2–3 minutes more. Do not boil after adding cream.
Season and brighten: Remove the bay leaf. Add salt and pepper to taste.
Finish with a squeeze of fresh lemon juice to balance the richness.
Serve: Ladle into bowls and top with chopped parsley. Add extra pepper if you like a little kick.