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To make the cake, preheat oven to 350 degrees. Grease and flour three 8 inch round cake pans.
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In a medium-sized bowl, whisk together flour, baking powder and soda, and salt. Set aside.
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In the bowl of your mixer, cream butter, oil, and brown sugar together until light and fluffy, about 4 minutes.
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Add the egg whites and beat until fully incorporated.
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Add the whole eggs and vanilla and beat mixture on medium-high speed for 4-5 minutes, or until light and airy.
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Beat in the flour mixture in 3 batches, alternating with the buttermilk, beginning and ending with flour, until just smooth and just combined. Do not overmix.
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Divide the batter evenly between the prepared pans. Bake until the cakes are lightly golden on top and a toothpick inserted into the center comes out clean, about 27-29 minutes.
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Let cakes cool in the pan for 10 minutes then remove from pan and let cool completely on a wire cooling rack.
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To make the filling, melt butter in a medium sized pot. Add peaches and brown sugar and cook on medium heat, stirring regularly, until peaches begin to break down, about 5 minutes.
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In a small bowl, whisk together corn starch and water. Pour into peaches and stir to combine. Cook peach filling for an additional 3-4 minutes or until mixture begins to thicken. Remove from heat and transfer to a bowl to cool completely before using.
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To make the frosting, cream together butter and jam until smooth. Add powdered sugar, salt, cream, and vanilla and beat on low until combined.
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Once combined, increase mixer speed to high and beat the frosting for an additional 3-4 minutes, or until light and airy.
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To assemble the cake, level cakes by cutting off domed tops, if necessary. If wanting a tall cake, slice layers in half.
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Place the first cake layer on a cake plate or cake board. Using an offset icing spatula, spread about ½ cup of the peach frosting over the cake layer.
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Pipe a rim of the frosting around the edge of the cake.
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Evenly spread about ¼ cup to ½ cup of the peach filling inside the frosting barrier.
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Repeat with remaining layers.
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After you place the final layer, frosting the outsides of the cake. Refrigerate the cake for at least 20 minutes to allow frosting to set.
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Right before serving, garnish with fresh peaches and granola for an added crunch.