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Preheat oven to 325 degrees F. Grease a 9x9 inch baking pan well.
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Cream together the butter and sugar until light and fluffy.
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Add the eggs one at a time, beating well after each addition.
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Beat in the vanilla extract and lemon zest.
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Sift together the flour and baking powder.
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Add the dry ingredients alternately with the milk, beginning and ending with the dry ingredients. In general, I add the dry ingredients in 3 portions and the milk in 2 additions.
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Quickly fold in the blueberries.
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Spread batter evenly into the prepared pan.
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Bake at 325 degrees F in a 9 inch well greased square pan for about 40 to 45 minutes or until a toothpick inserted in center comes out clean.
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The baking time can vary, especially if you use frozen berries. In that case it may take 10 or even 15 minutes more to bake. The toothpick test is the best way to ensure that this cake is fully baked. Let the cake rest for 15 minutes in the pan before pouring on the lemon drizzle glaze.