Heat the chicken broth in a medium saucepan until it starts to simmer.
While the broth warms, melt 1 tablespoon of butter in a large pot over medium-low heat. Add the asparagus with salt and pepper then cook frequently stirring until the asparagus is tender but still crisp, about 2 to 4 minutes depending on thickness. Stir in the peas and cook until just thawed, about 1 minute more. Remove the vegetables from the pot and set them aside.
Next, melt 2 tablespoons of butter in the same pot over medium-low. Add the chopped onion and cook, stirring often, until it becomes translucent, around 2 to 3 minutes. Add the minced garlic and cook for an additional minute without letting it brown.
Add the Arborio rice and stir continuously until the grains look glossy and somewhat translucent at the edges, approximately 2 minutes. Pour in the white wine, stirring until it has fully evaporated, about 1 minute.
Begin adding the simmering broth to the rice one cup at a time, stirring frequently and waiting until the liquid is mostly absorbed before adding the next. Continue this process for about 25 minutes until the rice is creamy and cooked to al dente.
Return the cooked asparagus and peas to the pot, then stir in the grated Parmigiano-Reggiano and the last tablespoon of butter. Taste and season with additional salt and freshly ground pepper as needed. If the risotto is overly thick, loosen it up with a splash of milk.
Serve immediately, spooning the risotto into bowls and offering extra Parmigiano-Reggiano alongside.