1. Cook the asparagus tips in a medium saucepan of boiling salted water until just tender, about 2 minutes. Using a slotted spoon, transfer the tips to a colander.
And rinse in cold water; drain well.
2. Break the asparagus stalks in half. Add them to the boiling water and cook until very tender, about 10 minutes. Reserve 1/3 cup of the cooking water, then drain the stalks. Puree the stalks with the reserved cooking water in a food processor. Using a rubber spatula, work the puree through a coarse sieve; you should have about 2 cups.
3. In a medium saucepan, bring the stock to a simmer. Meanwhile, heat the olive oil in a large, heavy saucepan. Add the shallots and cook over low heat, stirring frequently with a wooden spoon, until softened but not browned, about 4 minutes. Add the garlic and cook until the shallots are lightly browned, about 2 minutes. Add the rice and stir over moderate heat to coat the grains with the oil. Pour in the wine and continue stirring until the wine is almost evaporated, about 2 minutes.
4. Add 1 cup of the hot stock and stir constantly until almost absorbed. Continue adding the stock, 1 cup at a time, stirring constantly until it is absorbed before adding more. When the rice is almost tender, after about 15 minutes, add the asparagus puree. Continue to cook, stirring, until the rice is tender but still firm to the bite, about 4 minutes. Add the asparagus tips and stir for 1 minute to heat through.
5. Remove the risotto from the heat and stir in the butter and Parmesan. Season with salt and pepper and let stand for 2 minutes, then spoon the risotto into shallow bowls and serve.
This risotto gets its velvety texture from the asparagus puree that's stirred in before serving.