Bring a large pot of water to a boil. Then, add the chopped 1-inch pieces of asparagus stalks (reserving the tips). Cook for 1 minute. Then add the asparagus tips and cook an additional minute.
Once the asparagus has cooked for two minutes, strain into a colander then soak in an ice bath. Once the asparagus is chilled remove from the water and set to the side.
Combine the oil and onion in a large saucepan over medium heat and cook, stirring occasionally, until the onion is translucent, 2 to 3 minutes. Add the garlic and cook 1 minute.
Meanwhile, bring the 5 cups of stock to a simmer in a saucepan.
Melt 1 tablespoon of butter into the onions and garlic. Then add in the arborio rice. Cook on medium heat, stirring with a wooden spoon, until the rice is translucent, 1 to 2 minutes.
Add the wine and cook, stirring, until most of the liquid has evaporated, about 1 minute. Add ½ cup simmering stock and cook, stirring frequently, until most of the liquid has been absorbed, about 2 minutes.
Reduce the heat to medium-low, continue adding the broth, about ½ cup at a time, stirring frequently, until the rice is just tender and the mixture is creamy and has the texture of loose porridge, 17-20 minutes. Once the rice is fully cooked add the cooked asparagus and green peas. Mix well then season with salt and pepper, sprinkle with zested lemon peel and cheese. Mix well and serve.