Preheat oven to 375°F. Cook lasagna noodles in a large pot of salted water until al dente as per package instructions. Drain and rinse with cold water to prevent sticking. Shred the chicken.

In a large saucepan over medium heat, warm 1 Tbsp olive oil and sauté onions for 3-4 minutes until softened. Add 4 Tbsp butter, then whisk in 1/3 cup flour. Continue whisking for 3 minutes until the flour turns golden.

Pour in 2 1/2 cups chicken broth, 1 1/2 cups half and half, 2 tsp salt, and 1/2 tsp black pepper. Whisk until smooth and let it simmer for 5 minutes until it thickens to a light gravy consistency. Stir in minced garlic and chopped spinach, then remove from heat.

In a large bowl, combine ricotta cheese, egg, 2 cups of mozzarella cheese, 1/4 cup parmesan cheese, and 1/4 cup parsley.

Spread a small amount of bechamel sauce at the bottom of a 9x13 casserole dish. Lay 3 lasagna noodles on top. Spread half of the ricotta mixture over the noodles, followed by half of the shredded chicken. Pour 1/3 of the spinach sauce over the chicken. Repeat the layers: 3 noodles, the remaining ricotta mixture, the remaining chicken, and another 1/3 of the spinach sauce. Top with the last 3 noodles, pour the remaining spinach sauce, and sprinkle the reserved 1 cup of mozzarella cheese on top.

Place toothpicks over the lasagna to keep the foil from touching the cheese, then cover with foil. Bake in the preheated oven at 375°F for 45 minutes. Uncover and broil for 2-3 minutes until the cheese is browned. Let it rest for at least 10 minutes before slicing.