Heat a large stock pot over medium heat. Add butter and melt. Add garlic and saute for 2 minutes. Sprinkle in flour and whisk into butter. Cook for 2 minutes. Whisk in the chicken broth. Cook until slightly thickened. Stir in half and half and bring to a heavy simmer.
Once simmering, stir in lasagna noodles. Cook for 10 o 12 minutes, until noodles are tender. Remove from heat and stir in the chicken, mozzarella, ricotta and parmesan. Ladle into bowls and top with more shredded parmesan, if desired.