Cover a baking sheet with aluminum foil and preheat the oven to 425°F (220°C).
Coat the asparagus spears with extra virgin olive oil and fresh black pepper in a large bowl or baking dish. The cured ham and Manchego cheese are both salty, so skip adding extra salt here.
Wrap each asparagus spear with cured ham. If your ham slices are very large, you may only need to use half of a slice per spear. Roll on the diagonal to fully wrap the asparagus.
Place each wrapped spear on the baking sheet, making sure they aren’t touching one another, or they’ll steam instead of getting crispy.
Drizzle lightly with olive oil, then bake for 5 minutes in the middle of the oven.
Flip each asparagus spear, top with grated Manchego as desired, and bake for another 5 minutes, or until browned. If the spears don't brown, broil until the spears are golden on top.
Remove the pan from the oven and let them cool slightly. Serve the asparagus immediately, or reserve and reheat quickly before serving.