Rinse rice in a fine mesh strainer under hot running water until water runs clear, about 3 minutes.
Spray the slow cooker with olive oil or nonstick spray, or use a crockpot liner to prevent food from sticking.
Layer the rice in the bottom of the pot, followed by the chicken. Season with salt and pepper.
Add the onion, celery, peas and carrots, garlic and thyme. Add 2 ½ cups of chicken broth and push the veggies down to make sure they are covered.
Cover and place the slow cooker on low for 2 ½ - 3 hours, stirring every 30-40 minutes. Keep in mind that every time you lift the lid, you add about 15 minutes to the cooking time.
Start checking for doneness at 2.5 hours, and continue cooking until rice is tender and broth has been soaked up.
Once the rice is cooked to your liking (around 3 hours on low setting), in a small bowl stir together the remaining ½ cup of chicken broth, greek yogurt, parmesan cheese, and milk.
Gently stir the mixture into the casserole with a spatula and continue cooking on low setting for 20 to 30 minutes, until the rice is fluffed and creamy. Taste and adjust seasoning to taste, serve immediately, garnished with fresh parsley if desired.
Notes
Layer the ingredients exactly as listed in the recipe. It's important that the rice be placed on the bottom so that it can absorb the liquids properly.
Avoid cooking on high power. Set the slow cooker to low power for 3 to 3.5 hours. Using high power will overcook the rice, turning it to a mushy mess.
Start checking for doneness at 2.5 hours. If additional time is needed, continue to cook until the rice is tender and has absorbed most of the liquid. Try not to check too much, because every time you remove the lid, heat will escape from the slow cooker.
Why is my rice still hard, or too mushy? Slow cooker models are all different and you may need to adjust the time or liquid measurements slightly to suit your slow cooker. If your rice is cooked through, but there’s still excess broth in the slow cooker, simply ladle some out. Keep in mind that more liquid will be absorbed as it cools.