Preheat the oven to 350°F (175°C).
In a large oven-safe skillet or casserole dish, melt the butter over medium heat.
Add the chopped onion and cook, stirring occasionally, until softened and translucent, about 5 minutes.
Add the minced garlic and cook for 1 minute until fragrant.
Stir in the uncooked rice and cook for 2 minutes, stirring frequently to coat the rice in butter and lightly toast it.
Pour in the chicken broth, whole milk, heavy cream, lemon juice, and add the lemon zest, salt, black pepper, and dried thyme. Stir well to combine.
Bring the mixture to a gentle simmer, then remove from heat.
Stir in the cooked chicken and half of the shredded cheddar cheese.
Sprinkle the remaining cheddar cheese and the Parmesan cheese evenly over the top of the casserole.
Cover the casserole dish tightly with aluminum foil.
Bake in the preheated oven for 35 minutes.
Remove the foil and bake uncovered for an additional 10 minutes, or until the cheese is melted and golden and the rice is tender.
Remove from the oven and let the casserole rest for 5 minutes.
Sprinkle chopped fresh parsley over the top before serving.