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1
Preheat the oven to 350F. Line the bottom of an 8 1/2 x 4 1/2-inch loaf pan with parchment paper. Butter the pan and the paper.
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2
In a bowl, sift together the flour, baking powder, and salt.
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3
Fill a medium saucepan with 2 inches of water and bring it to a simmer. In the bowl of an electric mixer, combine the eggs, granulated sugar, and lemon zest. Set the bowl over the saucepan of simmering water and whisk until the mixture is warm to the touch, about 2 minutes. Transfer the bowl to an electric mixer fitted with the whisk attachment. Beat on medium speed until the mixture thickens, is pale yellow, and forms ribbons when the whisk is lifted, about 5 to 6 minutes.
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4
Meanwhile, in another bowl, whisk together the extra virgin olive oil, milk, and lemon juice. When the egg mixture has thickened, slowly drizzle in the oil mixture with the machine running. Reduce the speed to low, add the flour mixture, and mix just to combine. Drizzle in the melted butter and mix just to combine.
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5
Pour the batter into the prepared pan and sprinkle the top with the Demerara sugar. Bake, rotating the pan once after 40 minutes, until the top of the cake is golden, the center bounces back when touched, and a cake tester inserted in the center comes out clean, about 50 minutes. Unmold the cake from the loaf pan and let it cool completely on a wire rack. While still warm, prepare the glaze.
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6
Mix the water with powdered sugar until completely combined, without lumps. You might need to play with the consistency a bit to get it to your liking. Pour over the pound cake and let it dry, which should be fairly quickly. Once at room temperature, eat away!
