Cut the woody stem ends from each spear and reserve. Cut the remaining tender stalks into 1/2-inch pieces. In a medium pot, bring the stock to a boil. Add the tough woody stems, lower the heat and simmer to infuse with asparagus flavor, 20 to 30 minutes.Remove with a slotted spoon and discard, reserving the stock.Add the decorative tips to the stock and blanch until tender, 1 to 1 1/2 minutes. Remove with a strainer and refresh in an ice water bath.dd the tough woody stems, lower the heat and simmer to infuse with asparagus flavor, 20 to 30 minutes. Remove with a slotted spoon and discard, reserving the stock. Add the decorative tips to the stock and blanch until tender, 1 to 1 1/2 minutes.