Bring the broth to a simmer in a medium saucepan. Heat the oil in a heavy saucepan over moderately low heat and cook the onion, stirring occasionally, until soft, 3 to 5 minutes. Add the rice and cook, stirring constantly, 1 minute. Add wine and simmer, stirring constantly, until absorbed, about 1 minute. Add 3/4 cup of the hot broth, the salt and a few grinds of fresh pepper and simmer, stirring constantly, until broth is absorbed. Continue simmering and adding hot broth, about 3/4 cup at a time, stirring constantly and allowing the broth to be absorbed before adding more, until rice is almost tender and creamy-looking, about 18 minutes.
Add the spinach and peas and cook until the spinach is wilted. Add the asparagus and cook just until the vegetables are hot. Stir in the Parmesan and more broth if the risotto seems too thick. Serve in soup plates.