Coarsely grate the potatoes and zucchini in a medium sized bowl. Transfer to a colander and use the back of a ladle to squeeze out as much excess moisture as possible. Pat the grated potato and zucchini with paper towel and transfer back to the bowl. Set aside.
Melt the butter in a non-stick frying pan over medium heat. Add the leek and cook for 3 minutes or until soft (do not brown), then remove from the heat. Allow to cool slightly, then transfer the cooked leeks and any remaining butter to the bowl with grated potato and zucchini. Stir in self-raising flour, Parmigiano Reggiano, egg and parsley to combine. Season well with salt and pepper to taste.
To cook the frittelle (fritters), heat sesame oil in a large frying pan over medium heat. Add portions of the frittelle mixture (the size of 2 heaped tablespoons) to the frying pan. Flatten with a slotted turner or spatula. Cook until golden brown and cooked through (approximately 2 to 3 minutes on each side). Transfer to a plate lined with paper towel. Add more sesame oil if required, and repeat with the remaining frittelle mixture. Serve immediately – buon appetito.
2 zucchini (courgette) (about 350g), ends trimmed|2 desiree or sebago (brushed) potatoes (about 400g), peeled|40g unsalted butter|½ leek, cut in half lengthways and chopped|75g self-raising flour (alternatively 75g plain flour and ½ teaspoon baking powder)|50g Parmigiano Reggiano, finely grated|1 egg, lightly beaten with a fork|2 tablespoons flat-leaf parsley|Sesame oil for frying|Sea salt, freshly ground black pepper