Place all soup ingredients into your high speed mixer. Start on the lowest setting and gradually turn up the speed until the carrots are broken up pretty small. Turn mixer to high and blend until completely smooth. Transfer contents to a bowl or other container and place in refrigerator until chilled.
Place topping ingredients into food processor and pulse until mint is chopped small and all is combined. Transfer to another container and place in fridge.
To serve, label soup into a bowl and top with the yogurt. Garnish with mint, if desired.