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For the cake:
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Preheat oven to 325u00b0F.
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Butter and flour two 8- or 9-inch round cake pans.
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In a mixing bowl, whisk together the flours, baking powder, salt and cinnamon. Set aside.
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In a large bowl, cream together the butter and sugar until fluffy and pale in colour. Beat in the eggs one at a time, fully incorporating each egg and scraping down the bowl between each addition. Then add the vanilla. Next, add about 1/3 of the milk, beat to incorporate, then add 1/3 of the flour, again beating to incorporate. Repeat this process, scraping down the sides of the bowl as necessary, until all of the milk and flour are added and mixed in evenly.
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Divide the batter evenly between the two pans and bake in the preheated oven, rotating midway through, for about 35 minutes or until the cake tests done.
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Let the cakes cool in the pans on a rack for 5 minutes before turning them out onto the racks to finish cooling.
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To make the buttercream:
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Beat together the butter, brown sugar and cinnamon until fluffy and pale in colour. Add 6 cups of the confectioner's sugar and the vanilla extract and beat, starting on low and moving up to high, until it is fully incorporated. Scrape down the bowl and add the half and half. Beat to incorporate again. Add another 2 cups of the confectioner's sugar and beat, starting on low and moving up to high, until fully incorporated.
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Check the consistency of the buttercream. If it needs to be thicker, add the remaining confectioner's sugar. If it is too thick, add more half and half a teaspoon at a time, beating after each addition, until it reaches the consistency you like.
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To assemble and frost the cake:
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Level out your cooled cakes (cut a sliver of the round top off so that the top is level) and then cut each cake, horizontally, into two even layers (so you'll have 4 layers total).
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Place one layer on a cake plate then add a layer of buttercream, spreading to the edges and evening out as you go. Repeat the process as you add the remaining layers.
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Frost the top and sides of the cake with the remaining buttercream.
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If desired, garnish the top of the cake with whole cinnamon sticks.
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Cover and refrigerate for at least an hour before slicing.
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Store leftovers tightly covered in the refrigerator.
