Melt the butter in a large saucepan over medium heat, add the asparagus and onion, and cook for 10 minutes until the asparagus is tender.
Add the chicken stock, increase the heat to high, and bring to a boil. Add the peas and cook for 3 minutes, until the peas are tender.
Remove pot from the heat and add the mint, salt, and pepper.
Using a food processor or high-speed blender, puree the soup in batches. Pour the soup into a large bowl and repeat until all the soup is pureed.
Whisk in the heavy cream and taste for seasoning. Serve hot.