Step 1

Melt the butter in a large heavy-bottomed pot or Dutch oven over medium heat. Add the onion, thyme, and 1/2 teaspoon of the salt, and cook, stirring occasionally, until the onion is softened, about 8 minutes.

Step 2

Add the rice and garlic and cook, stirring occasionally, until they smell toasty, about 1 minute. Add the broth, milk, and remaining 1 1/2 teaspoons of salt, and season with pepper. Bring to a boil, stirring occasionally so that the rice doesn't stick to the pot. Add the chicken, stir to combine, and bring back to a boil. Reduce the heat to medium-low, cover, and simmer until the liquid is absorbed and the rice is tender, about 15 minutes. (Add water as needed if the rice absorbs it all before tender. If you'd like a browned top on the casserole, heat the broiler to high now.)

Step 3

Remove from the heat. Stir in the peas and 1 cup of the cheese. Taste and season with more salt as needed. Sprinkle with the remaining 1/2 cup cheese, then cover again and let sit for the cheese to melt and the rice to steam, about 5 minutes. (For a browned top, place under the broiler for a few minutes until the cheese turns golden-brown in spots.) Serve immediately.