In a large Dutch oven or oven-safe pot, heat olive oil over medium heat. Add the onion and sauté until softened, about 5 minutes.
Add the garlic and rice. Stir frequently until the rice starts to lightly toast, about 2 minutes.
Pour in the chicken broth, milk, and cream of chicken soup. Stir to combine. Season with salt and pepper.
Nestle the chicken into the mixture and bring it all to a simmer.
Cover the pot and transfer to a preheated oven at 375°F. Bake for 35 minutes.
Remove the lid, stir in the peas and Parmesan, then bake uncovered for another 10 minutes.
Let it sit for a few minutes before garnishing with parsley and serving.