Cook the Noodles: Bring a large pot of salted water to a rolling boil. Add lasagna noodles and cook until al dente, about 8-10 minutes. Drain and lay flat.

Prepare the Chicken Filling: In a bowl, combine shredded chicken, cream cheese, mozzarella, and chopped Hatch chiles. Mix until blended and creamy. Season with salt and pepper.

Make the Sauce: In a skillet, melt butter over medium heat. Add flour, whisk for 2-3 minutes. Gradually stir in milk, cooking until thickened, about 5-7 minutes. Stir in Parmesan cheese.

Preheat the Oven: Preheat to 350°F (175°C). Spread a thin layer of creamy sauce in a 9x13-inch baking dish.

Layer the Lasagna: Add a layer of noodles over the sauce, spread half of the chicken filling, drizzle with sauce, then repeat. Finish with a layer of noodles topped with remaining sauce.

Add Cheese Topping: Sprinkle remaining mozzarella over the top. Optionally add more Parmesan cheese.

Bake the Lasagna: Bake in preheated oven for 30-45 minutes until bubbly and golden. Cover with foil if browning too quickly.

Let it Rest: Once baked, let the lasagna rest for 15 minutes before slicing.