In a large, thick-bottomed pan, heat the olive oil over medium heat.
Sauté the shallots, asparagus stems, and kaffir lime leaves for about 3 minutes, stirring occasionally.
Add the Arborio rice to the pan and cook, stirring constantly, for about 2 minutes until the rice becomes translucent and glossy.
Pour in the white wine and let it evaporate.
Gradually add the vegetable broth to the rice, stirring frequently, and cook until the rice is tender and creamy, adding more broth as needed.
During the last 5 minutes of cooking, add the asparagus tips and peas to the risotto and continue cooking until they are tender.
Stir in the coconut milk and chopped coriander.
Season the risotto with salt and pepper to taste.
Serve the risotto in deep bowls or dishes.