Soften the vegetables: Melt the butter in a large skillet over medium heat. Add the onion, carrots and celery, and cook until softened, about 6 minutes.
Add garlic and flour: Stir in the garlic and cook for 30 seconds until fragrant. Sprinkle in the flour and stir constantly for about 1 minute so it cooks off its raw taste.
Pour in the broth: Slowly whisk in the chicken broth, scraping up any browned bits from the bottom of the pan. Bring the mixture to a gentle simmer.
Cook the orzo: Stir in the orzo and simmer uncovered, stirring occasionally, until the pasta is tender and the liquid has thickened, about 10 minutes.
Add chicken and cream: Stir in the shredded chicken, heavy cream and thyme. Let the mixture bubble gently for 2 to 3 minutes until everything is heated through and the sauce coats the back of a spoon.
Fold in the peas: Remove the skillet from the heat and fold in the frozen peas so they stay bright green and tender-crisp.
Season and finish: Taste and season with salt and pepper as needed. Stir in parmesan cheese if using, for extra richness.
Rest before serving: Let the skillet sit off the heat for 5 minutes; the sauce will thicken slightly more as it cools. Serve warm.