Bring a large saucepan of salted water to a boil over high heat. Prepare a bowl filled with ice water.
Add the asparagus pieces and cook until the asparagus is tender, 2 to 3 minutes. Just before the asparagus is finished cooking, scoop out 1 tablespoon of the cooking water and set aside.
Drain and immediately plunge the asparagus into the ice water to stop the cooking.
Transfer the asparagus to the bowl of a food processor, along with the garbanzo beans, garlic, tahini, lemon juice, reserved cooking water, cayenne and salt. Process until the ingredients are well combined.
With the processor running, slowly pour in the olive oil. Process until smooth.