Place lasagna pasta sheets into the bottom of a pan. Pour hot tap water directly over the noodles, making sure the pasta is completely immersed in the water. Let them soak for 30 minutes, then drain and discard water.
Preheat oven to 375 degrees. Lightly grease a deep 9x13 pan.
For the spinach artichoke filling: In a mixing bowl, mix together cream cheese, ricotta, mayonnaise, Parmesan cheese, garlic, basil, salt, and pepper. Gently stir in artichoke hearts and spinach. Set aside.
For the bechamel: melt butter in a medium sized saucepan over medium high heat. Whisk in flour and cook 2 minutes to brown. Slowly whisk in milk. Season with salt and pepper to taste.
To assemble, spread about 1 cup of bechamel in the bottom of the prepared pan. Place 4 noodles on top to cover. Spread with 1/3 of the spinach artichoke mixture. Top with 1/2 of mozzarella cheese. Spoon 1 1/2 cups bechamel over mozzarella, then sprinkle with 1/4 cup parmesan cheese. Repeat layering two more times to create three complete layers. To finish, place a final layer of pasta, topped with another 1 cup of bechamel to cover the pasta. Top with remaining mozzarella and Parmesan cheese. Cover loosely with aluminum foil.
Bake in preheated oven for 25 minutes. Remove foil, and bake an additional 25 minutes to allow cheese to brown. Serve hot.