Preheat oven to 350°F and cook lasagna noodles according to package directions, drain and set aside.
Pat shrimp completely dry with paper towels, then chop into bite-sized pieces and set aside.
In a large saucepan, melt butter over medium heat, add garlic and cook for 1 minute until fragrant.
Whisk in flour and cook for 2 minutes, then gradually add milk and cream, whisking constantly until sauce thickens, about 8 minutes.
Season white sauce with salt, white pepper, and nutmeg, then stir in half of the Parmesan cheese.
Add chopped shrimp to the sauce and cook for 3-4 minutes until shrimp turn pink and are just cooked through.
In a bowl, mix ricotta cheese with egg and half of the fresh parsley.
Spread a thin layer of shrimp sauce in a 9x13-inch baking dish, then layer 4 noodles, half the ricotta mixture, one-third of shrimp sauce, and one-third of mozzarella.
Repeat layers once, then top with remaining noodles, sauce, mozzarella, and remaining Parmesan.
Cover with foil and bake for 35 minutes, then uncover and bake 15 more minutes until golden and bubbly.
Let rest for 10 minutes, garnish with remaining fresh parsley and serve.