Preheat oven to 350 degrees F. Melt butter in a medium saucepan over medium heat.
Add onions, garlic and Italian seasoning and cook, stirring occasionally, until vegetables onions are softened, about 3 minutes.
Stir in flour until completely combined, then whisk in milk and chicken broth. Increase heat to medium high, bring mixture to a boil then reduce to a simmer. Cook, whisking occasionally, until thickened about 3-5 minutes. Stir in shrimp, 2 tablespoons parsley, 1/2 teaspoon salt and 1/4 teaspoon pepper and cook for 1 minute until shrimp is just starting to turn pink. Turn off heat and set aside.
In a medium bowl, stir to combine ricotta, 1/2 cup parmesan cheese and egg until smooth.
To assemble lasagna, in a 9x13 (un-greased) baking dish, spoon 1/2 cup shrimp sauce into the bottom of the dish. Top with 3 noodles. Spread 1/3 of the ricotta over the noodles, top with 1/3 of the shrimp and sauce and 1 cup shredded mozzarella. Top with 3 more noodles and repeat layering the ricotta, shrimp with sauce and mozzarella. Top with the last 3 noodles, the rest of the ricotta, the shrimp with sauce and mozzarella. Sprinkle the top with 1/4 cup parmesan, transfer to the oven and bake until bubbling and starting to brown, about 40-45 minutes.
Let cool 5-10 minutes before cutting. Garnish with 1 tablespoon chopped parsley and serve.