In a medium saucepan, over medium heat, melt the butter. Stir in the flour and cook for 2 minutes. Whisk in the milk, 1/2-cup at a time. Season with salt, pepper and nutmeg. Cook, stirring constantly for 4 to 6 minutes.
Remove from the heat and whisk in the cheese. Set aside and keep warm. Bring pot of salted water to a boil. In a large saute pan, over medium heat, add the oil. When the oil is hot, add the corn. Season with salt and pepper. Saute the corn for 6 minutes.
Add the spinach, a handful at a time. Season with salt and pepper. Saute for 2 minutes. Add the garlic and crabmeat. Season with salt and pepper. Saute for 2 minutes. Remove from the heat and keep warm. Add the pasta to the water and cook until tender, about 4 to 6 minutes. Drain and toss with olive oil. Season with salt and pepper.
To assemble, place four pieces of the pasta in the center of each plate. Place about 1/4 cup of the spinach filling over each piece of pasta. Place a piece of pasta over the spinach filling. Place a second 1/4-cup of the spinach filling over each piece of pasta. Place the remaining pieces of pasta over the filling forming 5 layers total. Spoon the sauce around the pasta. Garnish with parsley.