Center a rack in the oven and preheat the oven to 350°F. Butter four 5x3-inch mini loaf pans (you can use foil pans), dust with flour and tap out the excess (or use baker's spray). Place the pans on a baking sheet.

Whisk the cornmeal or polenta, flour, cornstarch, baking powder and salt together in a small bowl.

Put the sugar and lemon zest in the bowl of a stand mixer or, if you will be using a hand mixer, a large bowl. Use your fingertips to rub the ingredients together until the sugar is fragrant and moist. If using a stand mixer, fit it with the paddle attachment and attach the bowl. Drop the eggs into the bowl and, working on medium speed, beat until pale and slightly thickened, about 4 minutes. Lower the speed and add the vanilla and lemon juice. With the machine on low, add the cornmeal mixture and mix until it disappears into the batter. Add the melted butter in a slow, steady stream, mixing until combined, then do the same with the olive oil.

If using the berries, divide half of the batter evenly among the prepared pans. Sprinkle the berries into the pans and then pour the rest of the batter; the pans will be about three-fourths full. If not using berries, just divide the batter among the pans.

Bake the cakes for 30-35 minutes, until they are golden brown and a skewer inserted into the center comes out clean; the cakes will have started to pull away from the sides of the pans. Transfer the pans to a rack and cool for 5 minutes, then unmold, running a knife around the sides of the cake if needed. Allow the cakes to cool completely on the rack.

Dust the tops of the cakes with confectioners' sugar, if you'd like.