Cook the pasta according to the package directions.
In a medium sauce pan, melt butter on medium heat. Stir in minced garlic and flour and cook, stirring constantly, until bubbly.Gradually stir in milk, broth, salt and pepper.Cook and stir 2 - 3 minutes. Remove from heat and set aside.
Drain the pasta, rinse with cold water, and drain again.In a medium bowl, mix beaten egg, Parmesan cheese, and ricotta cheese and set aside.
Whisk together the broth mixture, the cheese mixture, and the pasta.
Pour the pasta mixture into the two prepared dishes, divided evenly.
Layer the shrimp over the pasta mixture, divided evenly in the two dishes.
Sprinkle on shredded mozzarella cheese and chopped fresh parsley and bake.