Using Y-peeler or vegetable peeler, shave asparagus into long, thin strips, transfer to large bowl and set aside.
In 12-inch (30 cm) skillet, heat 1 tbsp of the oil over medium heat until it shimmers. Add prosciutto and cook until golden and crispy, 2 to 3 minutes. Remove from skillet and place on paper towel-lined plate.
Add almonds to pan, toss to coat in the prosciutto oil and cook, stirring frequently, until toasty and golden, about 3 minutes. Transfer to cutting board, and when cool enough to touch, roughly chop nuts. Using your hands, tear prosciutto into bite-size pieces.
Season asparagus with salt and pepper. Add half the cheese, half the nuts, half the prosciutto and half the herbs and toss with the remaining 2 tbsp olive oil and the lemon juice. Taste and adjust with more salt if needed. Top with remaining cheese, nuts, herbs and prosciutto.