Make the béchamel. Melt butter in a medium heavy saucepan over medium-low heat. Add flour and whisk continuously for 3 minutes to cook the raw flour taste. Slowly whisk in the milk. Turn heat to medium-high and whisk until the sauce simmers and thickens, about 3 minutes. Season with 1/4 teaspoon salt, 1/8 teaspoon pepper and a pinch of nutmeg. Remove from heat and set aside.

Preheat the oven to 450°F (232°C).

Make the ricotta filling. In a medium bowl, combine ricotta, drained spinach, 1 cup Parmesan, chopped prosciutto, beaten egg, 3/4 teaspoon salt, and 1/2 teaspoon pepper. Stir until evenly mixed. Taste and adjust seasoning.

Cook the noodles. Bring a large pot of salted water to a boil. Add 1–2 tablespoons olive oil and the lasagna noodles. Boil until just tender but still firm to the bite (al dente). Drain and spread noodles in a single layer on a baking sheet so they don’t stick.

Prepare the baking dish. Butter a 13x9x2-inch glass baking dish. Pour the béchamel into the bottom and spread it into an even layer.

Lay one noodle at a time on your work surface. Spoon about 3 tablespoons of the ricotta mixture near one short end and spread into a thin strip about 1–2 inches wide. Roll the noodle from that short end into a tight log. Place each roll seam-side down on the béchamel in the dish. Repeat until you have 12 rolls.

Spoon 1 cup of marinara evenly over the rolls. Sprinkle the mozzarella and the remaining 2 tablespoons Parmesan on top. Cover the dish tightly with foil.

Bake covered for about 20 minutes, until the rolls are heated through and the sauce bubbles around the edges. Remove the foil and bake another 15 minutes until the top is golden and the cheese is bubbly. Let the dish rest for 10 minutes before serving.