Almond Cake:
Preheat the oven to 350°F (180°C) and line two 8-inch round cake pans with parchment paper. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, combine the cake flour, granulated sugar, baking powder, and salt. Mix on low speed until fully combined.
Add the softened butter to the dry ingredients and mix on low speed for 3-5 minutes, or until the mixture resembles wet sand.
Add the oil, eggs, egg white, vanilla extract, and almond extract, and mix until a thick batter forms. Slowly stream in the buttermilk and mix until fully incorporated.
Divide the batter evenly between the prepared pans and bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean.
Let the cakes cool in the pans for 10 minutes, then transfer them to a wire rack to cool completely.
Toasted Almonds:
Preheat the oven to 300°F (150°C).
Spread the sliced almonds in a single layer on a lined baking sheet. Bake for 15 minutes, stirring occasionally, until golden brown.
Almond Buttercream Frosting:
In the bowl of a stand mixer, beat the unsalted and salted butter on medium-high speed for 10 minutes, occasionally scraping down the sides of the bowl.
Gradually add the powdered sugar, 1 cup at a time, mixing on low speed. Once all the sugar is incorporated, mix in the almond extract.
Add heavy cream, 1 teaspoon at a time, until the frosting reaches your desired consistency.
Assembly:
Place one cake layer on a cake stand and spread ½ cup of frosting over the top. Add the second layer, flat side up, and apply a thin crumb coat over the entire cake. Refrigerate for 20 minutes to set.
Once chilled, apply a thick layer of frosting over the cake. Press the toasted almonds into the sides and top of the cake, ensuring the entire surface is coated.
Slice and serve this delicious almond cake!