It took years to convince me that vegetables could belong in desserts. But Italy’s cucina povera, or peasant cooking tradition, is actually full of cakes with vegetables that perfectly embody the cuisine’s spirit: They use whatever is abundant and in season—not just fruit, but vegetables, too—in an inventive way, turning poor ingredients into rich treats. Now, my favorite cakes with vegetables don’t hide the veggies, but rather exalt them, as part of a balance of contrasting textures and interesting, sometimes unusual flavors. In the beginning, it was pumpkin that helped me get over my doubts. Even Pellegrino Artusi, the father of Italian cuisine and the author of “La Scienza in Cucina e l’Arte di Mangiar Bene” (1891), has a recipe for torta di zucca gialla, Italy’s version of the American pumpkin pie. The pumpkin is grated and cooked in milk, then mixed with sugar, finely chopped almonds, butter, breadcrumbs, eggs, …