To make the bechamel 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 degrees F.
Add a tablespoon or 2 of oil to a large pot of boiling salted water. Boil the noodles until al dente. Drain. Arrange the noodles in a single layer on a baking sheet or work service to prevent them from sticking.
In a medium bowl, stir together the ricotta, spinach, 1 cup Parmesan, prosciutto, egg, salt, and pepper. Mix until thoroughly combined.
Pour the bechamel sauce over the bottom of the prepared dish. Layout 4 lasagna noodles on a work surface, then spread a large spoonful (about 3 tablespoons worth) of ricotta mixture evenly over each noodle. Starting at 1 end, roll each noodle like a jelly roll. Lay the lasagna rolls seam side down, without touching, atop the bechamel sauce in the dish. Repeat with the remaining noodles and ricotta mixture. Pour the jar of marinara sauce evenly over the lasagna rolls. Sprinkle the mozzarella and the remaining 2 tablespoons of Parmesan over the lasagna rolls. Cover tightly with foil. Bake until heated through and the sauce bubbles for about 20 minutes. Uncover and bake until the cheese on top becomes golden, about 15 minutes longer. Let stand for 10 minutes.
Notes
To make these ahead of time. Fully assemble roll-ups in the 9X13" baking dish (without baking), cover tightly with foil, and refrigerate overnight. Bake as directed. It may be necessary to add 5 to 10 minutes to the cooking time since the rolls will be going into the oven cold.To freeze: Fully assemble roll-ups in a baking dish (without baking), cover tightly with foil, and freeze for up to 3 months. It is easy to freeze individual rolls for quick and easy meals later! Just put rolls into freezer containers and mark the date on the container so you know when they entered the freezer.To thaw &reheat. Thaw in the refrigerator for twenty-four hours or until thawed and bake as directed. To reheat individual containers, thaw, microwave for 3-5 minutes or warm them in the oven at 350ºF for 10-15 minutes.