For the sauce, melt the butter in a heavy medium saucepan over medium-low heat. Add the flour and whisk for 3 minutes.
Whisk in the milk. Increase the heat to medium-high. Whisk the sauce until it comes to a simmer and is thick and smooth, about 3 minutes.
Whisk the salt, pepper, and nutmeg into the bechamel sauce.
Preheat the oven to 450°F
For the lasagna mixture, whisk the ricotta, spinach, 1 cup Parmesan, prosciutto, egg, salt, and pepper in a medium bowl.
Add a tablespoon or 2 of oil to a large pot of boiling water. Boil the noodles until just tender but still firm to bite. Drain. Arrange the noodles in a single layer on a baking sheet to prevent them from sticking.
Butter a 13x9x2 inch glass baking dish. Pour the bechamel sauce over the bottom of the prepared dish.
Lay out 4 lasagna noodles on a work surface, then spread about 3 tablespoons of ricotta mixture evenly over each noodle. Starting at 1 end, roll each noodle. Lay the lasagna rolls seam side down and place in baking dish on top of bechamel sauce. Repeat with the remaining noodles and ricotta mixture.
Spoon 1-2 cups of marinara sauce over the lasagna rolls. Sprinkle the mozzarella and remaining 2 tablespoons of Parmesan over the lasagna rolls.
Cover tightly with foil. Bake until heated through and the sauce bubbles, about 20 minutes.
Uncover and bake until the cheese on top becomes golden, about 15 minutes longer. Let stand for 10 minutes.