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Preheat the oven to 300 degrees F.
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Grease and flour a 9'x9" pan.
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In a separate bowl, whisk together the flour, baking powder, and salt.
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Cream together the butter, 1/2 cup of the sugar, and vanilla extract. Add the eggs one at a time, making sure each is fully incorporated into the batter before adding the next.
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Add the dry ingredients and milk and mix until just combined.
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Spread the batter out onto the prepared pan. Place in the oven and bake for 20 minutes.
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Remove from the oven, let cool and then transfer the cake to a wire cooling rack.