Heat the olive oil in a large saucepan over medium heat. Add the onion and garlic, and cook until softened.
Add the Arborio rice and cook, stirring constantly, for 2-3 minutes until the rice is lightly toasted.
Begin adding the warm vegetable broth, one ladle at a time, stirring frequently. Allow the liquid to be absorbed before adding the next ladle.
After about 15 minutes, add the asparagus pieces. Continue to add broth and stir until the rice is creamy and cooked through, about 20-25 minutes total.
Stir in the frozen peas and cook for another 2-3 minutes until heated through.
Remove from heat and stir in the grated Parmesan cheese. Season with salt and pepper to taste.
Serve immediately, garnished with additional Parmesan cheese if desired.