Bring stock to a simmer in a medium saucepan.
Heat olive oil in a large saucepan or dutch oven over medium heat.
Add the onion, cooking until soft and translucent, about 4-5 minutes.
Then, stir in the minced garlic and sauté 1 minute longer.
Pour in the arborio rice and stir the rice until it is coated with the olive oil and onions. Toast the rice for about 2 minutes, stirring frequently.
Add the dry white wine and let cook for about 2 minutes, until the rice has absorbed the wine. Reduce the heat to medium-low heat.
Once the vegetable stock is simmering, carefully add 1/2 cup to the rice mixture. Stir continuously with a wooden spoon, until the stock is almost completely absorbed. Keep adding 1/2 cup stock at a time, stirring until almost absorbed before adding the next 1/2 cup.
On the last addition of stock, add the asparagus with the stock. This process of adding the stock will take about 20 minutes in total. The rice should be really creamy, yet still al dente.
Stir in the peas, lemon zest and grated parmesan cheese. Season with salt and pepper. Let cook an additional minute until the peas are heated through.
Portion out into bowls. Add 1-2 oz of burrata into each bowl. Serve with additional salt, pepper and lemon wedges if desired.