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Preheat the oven to 350 degrees F.
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To make the cake: In a large bowl, mix together the flour, baking powder, salt and orange zest.
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Set aside.
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In an electric mixer, combine the eggs and sugar and beat until light and fluffy.
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Add the oil and vanilla and beat until just combined.
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Beginning and ending with the dry ingredients, add the flour mixture in thirds, alternating with the 3/4 cup orange juice.
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Mix slightly after each addition, just to incorporate.
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Add the poppy seeds and mix to incorporate the seeds into the batter.
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Pour the batter into a greased 10-inch springform pan.
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Bake for 1 hour, or until the point of a knife inserted into the center comes out clean.
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To make the syrup: While the cake is baking, place the syrup ingredients into a small saucepan and heat until thickened, about 3-4 minutes.
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When the cake is done, immediately unmold it from the springform pan.
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Prick it all over with a skewer and brush the syrup all over the top and sides of the cake while it is still hot.
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The cake will absorb all the syrup.
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Let the cake cool completely before serving.