Cut zucchini with skin and peeled potato into cubes. Finely chop onion and garlic, salt and glaze in butter and oil in a heavy-bottomed skillet. Add potatoes and then zucchini and sauté for about 4 minutes, stirring occasionally.
Pour 1 cup broth, bring to a boil and braise covered for about 4 minutes, stirring occasionally. Pour remaining broth, cook until vegetables are tender for about 10 minutes.
Towards the end of cooking add mint and flour mixed with a few tablespoons of cold water. Bring soup to a boil and remove from heat.
Place yogurt in a cup and mix with a few tablespoons of soup, adding gradually. Mix into the soup and then blend everything, season with salt and pepper. Serve immediately, do not boil after adding yogurt, sprinkle with remaining mint. Serve with croutons: cut any type of bread into cubes, spread on a baking sheet and brown in the oven.