Make the sauce: Melt butter in a large saucepan over medium-high heat. Add garlic and saute until fragrant, stirring for 1 minute to avoid burning. Add flour, poultry seasoning, and salt. Whisk and cook for 1-2 minutes. Gradually add milk, whisking until smooth and thick, about 5-7 minutes. Remove from heat.
Layer the lasagna: Preheat oven to 400F (200C). Grease a 9x13 inch baking dish. Cover the bottom with about 5 broken lasagna noodles, half the shredded chicken, half the frozen peas, 1/4 cup Parmesan cheese, 1/3 cup water, and 1 1/2 cups sauce. Repeat this layer once more.
Top the lasagna: Add a final layer of broken noodles, 1/3 cup water, 1 1/2 cups sauce, and 1/2 cup Swiss cheese.
First bake: Cover the dish with foil and bake for 40 minutes.
Second bake: Remove the foil, sprinkle evenly with seasoned breadcrumbs, and bake for an additional 5-10 minutes until the top is golden brown and bubbly.
Garnish and rest: Sprinkle with fresh herbs like parsley and thyme. Let stand for 10 minutes or more before cutting and serving.