Peel and dice the shallots.
Peel the potatoes and cut into small pieces.
Wash the radishes and pat them dry. Trim the greens and chop them into small pieces.
Slice the red part of the radishes into rounds.
Heat the unsalted butter in a large saucepan over medium-high heat.
Add the shallots and stir fry until they become transparent.
Add the chopped parsnip and potato pieces to the pan and stir to combine.
Season with salt and freshly ground pepper.
Cook the mixture, stirring occasionally for 3 minutes.
Add the vegetable broth to the pan. Bring the mixture to a boil.
Lower the heat and let the mixture simmer for 15 -20 minutes or until the vegetables become soft. You should be able to run a fork through them easily.
Add the radish greens to the soup and cook for another 5 minutes.
Stir the heavy cream into the soup and let cook another 5 minutes.
Use a hand blender to puree the soup. If you do not have one handy, transfer the soup to a food processor or blender and puree, then transfer the pureed soup back into the saucepan.
Add the radish rounds and the chopped fresh mint into the soup. If you prefer, reserve some of the red round pieces for garnish.
Cook the soup for another 5 minutes.
Remove from heat and divide into 4 bowls.
Scatter the fresh red radish rounds and chopped mint or mint leaves over the top of the soup in each bowl and serve.