In a pot, heat a little olive oil over low heat. Add the shallot and sauté, stirring continuously, for a few minutes until softened.
Meanwhile, clean and dice the zucchini and potatoes.
Add the vegetables to the pot, pour in 3 ladles of broth, and stir. Cover with a lid and cook over medium heat for 20-25 minutes, or until the vegetables are tender. Add more broth as needed to keep the vegetables from drying out.
Once the vegetables are cooked, remove the pot from the heat and blend the mixture with an immersion blender until smooth. If the soup is too thick, add a little more broth. If it’s too thin, simmer it over medium heat until it reaches the desired consistency.
Serve the soup garnished with chopped mint and pepper to taste.