Melt the butter in a large saucepan over medium heat. Add the onion and cook until softened, 3 to 4 minutes.
Add the broth, peas, mint, salt, and sugar. Remove from heat.
Transfer half the mixture to a blender or food processor and puree until smooth. Repeat with the remaining soup.
To serve the soup cold, transfer it to a bowl, cover, and refrigerate for at least 3 hours and up to 24 hours.
To serve the soup hot, return it to pan and place over medium heat until warmed through. Ladle into teacups.