Preheat the oven to 350°F (175°C).
In a pot of lightly salted water, cook the lasagna noodles until al dente, approximately 8 to 10 minutes. Drain and rinse the noodles under cold water. Set aside.
In a large skillet, melt the butter over medium heat. Sauté the minced onion until softened and fragrant. Once tender, remove the skillet from the heat and stir in the cottage cheese, cream cheese, beaten egg, dried basil, salt, and pepper. Mix well until the ingredients are fully combined. Set this mixture aside.
In a separate large bowl, combine the cream of mushroom soup, cooked shrimp, crabmeat, milk, and dry white wine. Stir the ingredients together until the mixture is evenly blended. Set aside.
Begin assembling the lasagna by laying three cooked lasagna noodles at the bottom of a 9x13-inch baking dish. Spread a third of the onion and cheese mixture over the noodles, followed by a third of the seafood and soup mixture. Repeat this layering process two more times, finishing with a top layer of Cheddar and Parmesan cheeses.
Bake the lasagna in the preheated oven for approximately 45 minutes, or until the dish is heated through and bubbling.