Step 1Position a rack in the lower third of the oven and heat the oven to 325 degrees. Grease the sides of a 9-inch springform pan, or 9-inch-by-3-inch cake pan with a removable bottom, and line the bottom with parchment paper.
Step 2In a medium bowl, combine one-third cup of the sugar, the egg yolks, salt and both zests. In a standing mixer or with a hand-held mixer, beat at high speed until thick and light in color. Gradually beat in the olive oil, followed by the Vin Santo.
Step 3Put the egg whites and cream of tartar in a large bowl and beat (at high speed if using a hand-held mixer, medium speed if using a standing mixer) until soft peaks form when the beaters are lifted. Gradually beat in the remaining one-third cup sugar and continue to beat until the egg whites are stiff but still moist when the beaters are lifted.
Step 4Pour half the egg mixture over the egg whites, sift half the flour on top, and fold until nearly incorporated. Scrape the remaining egg mixture into the bowl and sift in the remaining flour. Fold just until the ingredients are blended.
Step 5Scrape the batter into the prepared pan. Bake until the cake is puffed and golden, about 30 minutes. Reduce the temperature to 300 degrees and bake until a thin wooden skewer inserted in the center of the cake comes out clean, 10 to 15 minutes. If the cake is browning too fast, place a piece of buttered parchment or wax paper on top. Cool the cake in the pan on a rack for at least 10 minutes, then remove it from the pan and cool on the rack. The cake stays moist for at least 2 to 3 days if refrigerated, tightly wrapped.