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Preheat the oven to 400°F. Butter or oil a 10-by-15-inch jellyroll pan or a 16-3/4 by 12-inch sheet pan.
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In a large bowl, combine the flour, baking soda, salt, granulated sugar, brown sugar, and cinnamon.
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In a medium saucepan over medium-high heat, combine the butter with 1 cup water and heat until the butter melts. Bring to a boil. Once the mixture is boiling, remove from heat and add in the flour mixture. Add in the buttermilk, eggs, and vanilla. Gently stir in the apples.
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Pour the batter into the prepared pan, spreading evenly. Bake for 20 minutes if using a jelly roll pan, and about 17 minutes if using a half sheet pan, or until a toothpick inserted comes out clean. Let cool in the pan on a wire rack for about 10 to 15 minutes.