Bring a large pot of water to a boil; cook asparagus until just tender, 3 to 4 minutes. Remove asparagus with a slotted spoon, keeping water boiling.
Heat a skillet over medium heat; cook prosciutto in hot skillet until crisp, 2 to 3 minutes. Remove prosciutto from skillet and transfer to a work surface to cool; chop.
Heat olive oil in a skillet over medium heat; cook and stir green onions until lightly browned, about 5 minutes. Remove skillet from heat; add asparagus.
Cook linguine in the pot of boiling water until tender yet firm to the bite, about 11 minutes. Drain pasta, reserving 1/4 cup of the pasta water.
Combine pasta, 1/4 cup pasta water, asparagus, and green onions together in a serving bowl; top with prosciutto.
