Preheat oven to 375°F (190°C). Grease a 9x13-inch baking dish.
Cook egg noodles according to package directions until al dente. Drain and set aside.
In a large pot or Dutch oven, melt butter over medium heat. Add onion and cook until softened, about 4 minutes. Add garlic and cook 1 minute more.
Stir in flour and cook for 1 minute, whisking constantly.
Gradually whisk in chicken broth, milk, and heavy cream. Bring to a simmer, stirring often, until thickened, about 3-4 minutes.
Remove from heat. Stir in salt, pepper, thyme, shredded chicken, peas (if using), and 1 cup of the cheddar cheese. Add cooked noodles and toss to combine.
Transfer mixture to prepared baking dish. Sprinkle remaining 1/2 cup cheddar cheese on top.
Bake for 20-25 minutes, until bubbly and cheese is melted and lightly golden. Let rest 5 minutes before serving.
Tips
For a crunchy topping, mix 1/2 cup panko breadcrumbs with 1 tbsp melted butter and sprinkle over cheese before baking.
Leftovers can be refrigerated for up to 3 days; reheat in the oven or microwave.