Heat the chicken broth in a medium saucepan until it reaches a gentle simmer.
Meanwhile, melt 1 tablespoon of butter in a large pot over medium-low heat. Add the asparagus along with salt and a few cracks of black pepper. Stir and cook until the asparagus is tender but still crisp, about 2 to 4 minutes depending on thickness. Add the peas and cook until thawed, around 1 minute. Remove vegetables from the pot and set aside.
In the same pot, melt 2 tablespoons of butter over medium-low heat. Add the chopped onions and cook, stirring frequently, until they become translucent, about 2 to 3 minutes. Stir in the minced garlic and cook for an additional minute without letting it brown.
Add the Arborio rice to the onions and garlic, stirring constantly until the rice looks glossy and the edges turn translucent, roughly 2 minutes. Pour in the white wine and let it cook until fully absorbed, about 1 minute.
Begin adding the simmering broth, about 1 cup at a time, to the rice. Stir occasionally and wait for the liquid to be mostly absorbed before adding more. Continue this process for about 25 minutes until the rice is creamy and just tender.
Fold the cooked asparagus and peas back into the risotto along with the grated Parmigiano-Reggiano and the last tablespoon of butter. Taste and season with extra salt and pepper if needed. If the risotto feels too thick, loosen it slightly with a little milk.
Serve the risotto hot in bowls and offer additional Parmigiano-Reggiano at the table for extra richness.