Preheat the oven to 400°. Set a wire rack over a baking sheet and set aside.
Add equal parts ice and water to a large bowl and set aside.
Bring a saucepan of salted water to a boil. Blanch the asparagus in the water for about 2 minutes, then transfer immediately to the ice bath. Remove from the ice bath and dry completely with paper towels.
Sprinkle the asparagus with pepper. Wrap each asparagus spear with Iberico ham, allowing the tip of the asparagus to show through at the top.
Lay 1 sheet of phyllo on a work surface with the short end in front of you. Brush it with butter and fold it over lengthwise. Brush it with butter and sprinkle with 1 tablespoon of parmesan cheese. Place an ham wrapped asparagus spear on the phyllo with the tip sticking out over the phyllo and begin to roll it up into the phyllo, brushing with a little butter to the phyllo sticks to itself as you roll. Brush with a little more butter and dust it lightly with more parmesan. Place the rolls onto the wire rack. Continue with the remaining asparagus.
Bake for 10 minutes, then turn the asparagus fingers over and bake for an additional 5-8 minutes until crisp and golden brown.
Cool for a few minutes before serving. Arrange them whole, or as the recipe suggests, slicing them on an angle into bite sized pieces.