Bring butter, cream and milk to a low simmer in a medium-sized heavy bottom pot. Remove from heat.
Place frozen peas in blender and gradually pour hot milk mixture over peas. If there is more liquid than your blender canister will hold, pour in batches. Place lid on top of blender, removing the center cap to allow the steam to escape.
Blend on low for five minutes, until mixture is well combined. Place a mesh strainer or sieve over a large heat safe bowl. Gradually pour soup mix into strainer, mashing to get all the liquid passed through. Repeat this process until all the soup mix has gone through the strainer.
Discard the pea pulp left in the strainer. Place the strainer soup back in the blender and add the Greek yogurt. Blend for one minute, or until smooth. Transfer soup mix to pitcher for easy pouring.
Cover with plastic wrap and chill for at least two hours or overnight. While soup is chilling, place mint leaves and olive oil in a small food processor, blend on high until well combined. Remove from food processor and set aside until ready to serve soup.
Once soup is chilled, pour individual servings, top with a dollop of reserved Greek yogurt and teaspoonful of mint oil.