Heat the olive oil in a stockpot over medium heat. Add the onion and sauté it, stirring occasionally, until tender, 7 to 8 minutes. Add the chicken stock and peas and bring to a simmer; then remove the pot from the heat.

Stir the half and half, and mint leaves into the soup mixture. Let cool at room temperature for a few minutes. Then, using an immersion blender, or working carefully in batches in a blender or food processor, puree the soup.

Transfer the soup to a covered container and chill in the refrigerator for 3 to 4 hours. Before serving, stir or shake the soup and ladle into chilled cups, mugs, or bowls. Serve immediately, garnished with mint leaves.