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Preheat the oven to 325°. Butter and flour an 8-inch fluted Bundt or tube pan. Butter the dull side of a 10-inch piece of foil.
In the bowl of an electric mixer fitted with the whisk, beat the sugar with the egg yolks and whole egg at medium-high speed until the mixture is pale yellow and very fluffy, about 8 minutes. Beat in the lemon zest. Sift the flour and cornstarch over the egg mixture and fold in with a rubber spatula. At medium speed, beat in the butter, then beat in the poppy seeds.
Pour the batter into the prepared pan and cover tightly with the buttered foil. Bake for 45 minutes, or until the cake pulls away from the side of the pan and a cake tester inserted in the center of the cake comes out clean. Remove the foil and let the cake cool in the pan on a rack for 15 minutes. Invert the cake onto the rack and let cool completely before serving, at least 30 minutes.
The cake can be wrapped in plastic and foil and left at room temperature for up to 3 days.