Preheat the oven to 350 degrees F. Generously butter and flour a 9-inch springform pan, tapping out any excess flour. Set aside.
In the bowl of an electric mixer fitted with the whisk attachment, beat the eggs and sugar until thick and lemon-colored, about 3 minutes. Add the butter, oil, milk, and vanilla extract, and mix until blended.
Sift the flour, baking powder, and salt into a large bowl. Add the lemon and orange zests, and toss to coat the zests with flour. Spoon the mixture into the bowl of batter and stir with a wooden spoon until thoroughly blended. Scrape down the sides of the bowl and mix once more. Set aside for 10 minutes to allow the flour to absorb the liquids.
Stir about 3/4 of the grapes into the batter. Spoon the batter into the prepared cake pan and smooth out the top with a spatula.
Place the pan in the center of the oven. Bake for 15 minutes, then sprinkle the top of the cake with the remaining grapes. Bake until the top is a deep golden brown and the cake feels quite firm when pressed with a fingertip, about 40 minutes more, for a total baking time of 55 minutes. Remove to a rack to cool. After 10 minutes, run a knife along the sides of the pan. Release and remove the side of the springform pan, leaving the cake on the pan base. Sprinkle with confectioner's sugar just before serving. Serve at room temperature, cut into thin wedges.
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