Prep the slow cooker: Lightly grease the insert or use a liner.
This helps prevent rice from sticking around the edges.
Layer the base: Add diced onion, carrots, celery, and garlic to the slow cooker. Sprinkle in thyme, parsley, smoked paprika, salt, pepper, and the bay leaf.
Add rice and broth: Rinse the rice under cold water until the water runs mostly clear. Add it to the slow cooker and pour in the chicken broth.
Stir to distribute everything evenly.
Nestle in the chicken: Place the chicken on top of the rice and veggies. Don’t cut it yet; large pieces stay juicier.
Cook: Cover and cook on Low for 4 to 5 hours or High for 2.5 to 3 hours, until the chicken is cooked through and the rice is tender. Avoid lifting the lid during the first few hours.
Shred and enrich: Remove the chicken to a plate and shred with two forks.
Stir the cream cheese, heavy cream, and butter into the slow cooker until melted and smooth.
Finish: Return the shredded chicken to the pot. Stir in frozen peas. Cover and cook on Low for another 10 to 15 minutes, just until the peas are warm and the mixture is creamy.
Adjust salt and pepper.
Serve: Spoon into bowls and top with chopped parsley. Add a squeeze of lemon if you like a little brightness.