Preheat the oven to 350°F. Spray an 8x8 square baking dish with baking spray, and set aside.

In a medium-sized bowl, stir together the flour, baking powder, baking soda, and salt, and set aside.

In the body of a stand mixer with the paddle attachment, beat together the butter, oil, and sugar until light and fluffy, around 3 minutes.

Add the egg yolks and egg one at a time, making sure to mix in the first one well until adding the next. Next, stir in the vanilla and almond extract.

Add half of the flour mixture and mix it in.

Add half of the buttermilk, and stir it in until combined. Repeat with the remaining flour and buttermilk, and scrape down the sides as needed.

Spread the batter into the prepared baking dish.

Bake for 26-28 minutes until light golden brown and it begins to pull away from the sides, a toothpick inserted into the center will come out clean. Let it cool in the pan completely.

Next, make the filling. Place the cornstarch, salt, and egg yolks into a medium-sized bowl and whisk until combined, set aside.

Place the milk and sugar into a small saucepan and stir to combine. Place over medium heat, stirring constantly until it comes to a simmer.

Once at a simmer, very slowly stream the milk mixture into the egg yolk mixture, whisking constantly until fully combined.

Pour the mixture back into the pot. Stirring constantly, bring to a boil.

Take off the heat and stir in the butter, vanilla, and almond extract.

Place a fine mesh strainer over a large bowl. Pour the filling through the strainer and press it through with a spatula or spoon to get any lumps out. Place a piece of plastic wrap touching the filling over top. Place in the refrigerator for 2 hours to chill completely.

For the almonds, line a sheet pan with parchment paper, and set aside. Place the almonds on the sheet pan in a single layer. Bake for 18 minutes, tossing the almonds around roughly every 3 minutes.

Place the almonds into a large bowl then add the water and sugar, stir to combine.

Place them back on the sheet pan in a single layer. Continue to bake for 12-15 minutes, stirring every 3 minutes until you reach your desired toastiness. Transfer immediately to a cold sheet pan to cool, or they will continue to toast.

For the frosting, in a large bowl with an electric hand mixer, beat the butter until smooth. Add the powdered sugar a little at a time until fully combined.

Add the salt, vanilla, almond extract, and milk, and stir until combined. Then place mixer on medium-high speed and beat for 3 minutes until light and fluffy.

Once the cake is completely cooled and the filling has chilled, assemble the cake. Take the cake out of the pan and cut it in half lengthwise. Place the bottom on your serving platter.

Spread and smooth the filling on top, leaving a ½-inch border. Place the top of the cake on top, and press down gently.

Add a thin layer of frosting all over creating a crumb coat. Place in the refrigerator for about 1 hour to set.

Add the remaining frosting to the outside of the cake. Take the almonds and press them all over the cake into the frosting so it will stick, serve immediately.