- Preheat an oven to 400°F. Butter a small roasting pan.
- In a sauté pan over medium heat, warm the olive oil. Add the onion, salt and pepper and cook, stirring frequently, until the onion is soft but not browned, 8 to 10 minutes.
- Add the garlic and cook for 1 minute. Transfer the onion mixture to a plate and let cool to room temperature.
- Lay 1 pasta sheet horizontally on a clean work surface. Scoop 2 tablespoons filling onto the right half of the sheet. Lay another pasta sheet over the filling, placing it perpendicular to the bottom sheet so it forms an "L" shape.
- Scoop 2 tablespoons filling onto the top pasta sheet, placing it directly over the bottom filling. Fold the bottom sheet over the filling and top with 2 tablespoons filling. Place 4 asparagus spears at an angle on top of the filling, then fold the remaining end of the pasta sheet over the asparagus.
- Drape 1 prosciutto slice over the lasagna, tucking the edges underneath, and place in the prepared pan. Repeat with the remaining ingredients to assemble a total of 4 lasagnas.
- Cover the pan with aluminum foil and bake for 20 minutes. Remove the foil and continue baking until the prosciutto is crisp and the filling is hot, 20 to 25 minutes more.
- Transfer the lasagnas to a platter and serve immediately.