Heat the stock and 2 cups (500 ml) water in a medium saucepan to just below a simmer. Cover; keep at a simmer.
Heat oil in a large, deep, non-stick frying pan over medium heat. Sauté onion until slightly softened, about 3 minutes. Add chopped mushrooms and garlic. Sauté until mushrooms soften, 5 minutes. Stir in the barley. Stir in 2 cups (500 ml) hot stock mixture. Simmer, covered, 15 minutes.
Blanch asparagus tips in the stock liquid in the saucepan for 2 minutes. Transfer to a plate with a slotted spoon.
Add more hot stock to the barley mixture, ½ cup (125 ml) at a time, stirring frequently. Each addition of liquid must be fully absorbed before any more is added. When adding the last of the stock, stir in asparagus stems and parmesan. Serve the risotto topped with asparagus tips.