Start with the chicken base Add the chicken, chicken broth, cream of chicken soup, milk, all spices, onion, garlic, and carrots to the slow cooker. Stir gently to combine.
Cook without the rice Cover and cook on LOW for about 3½ hours (or HIGH for 1½–2 hours), until the chicken is nearly cooked through and the carrots have started to soften.
Add the rice Rinse the rice under cold water until the water runs clear to remove excess starch. Stir the rice into the slow cooker, making sure it is fully submerged in the liquid. If your slow cooker runs hot, keep a close eye at this stage or switch to warm slightly earlier.
Finish cooking Cover and continue cooking on LOW for 45–60 minutes, until the rice is tender and the chicken is fully cooked. If cooking on HIGH, reduce the time to 25–30 minutes and check early.
Add the veggies Stir in the peas or broccoli, then cover and let sit for 5–10 minutes until just tender.
Make it creamy (optional) Stir in the shredded cheddar cheese just before serving, if using.
Serve and garnish Spoon into bowls and garnish with fresh parsley, extra cheese, or a squeeze of lemon juice if desired.