Preheat oven to 400°F (200°C). Grease a 9x13-inch baking dish or similar size casserole dish.
Cook Vegetables: In a large skillet, melt the butter over medium heat. Add the onion, carrots, and celery, cooking until softened, about 5-7 minutes. Stir in the garlic and cook for another minute.
Make Roux: Sprinkle the flour over the vegetables, stirring to coat. Cook for 2 minutes. Gradually whisk in the chicken broth and heavy cream, bringing to a simmer. Cook until the sauce thickens, about 3-5 minutes.
Add Chicken: Stir in the shredded chicken, peas, thyme, salt, and pepper. Simmer for 5 minutes, then transfer the mixture to the prepared baking dish.