Preheat the oven to 350°F (177°C). Grease three 8-inch round cake pans and line the bottoms with parchment paper to prevent sticking.

In a medium bowl, whisk together the cake flour, baking powder, baking soda, and salt.

In the bowl of a stand mixer fitted with the paddle attachment, beat the butter, sugar, and oil together on medium-high speed for 3 to 5 minutes, until pale and fluffy.

Add the eggs one at a time, beating well after each addition. Add the egg white and mix until incorporated.

Mix in the vanilla bean paste and almond extract.

With the mixer on low speed, alternate adding the dry ingredients and the buttermilk, beginning and ending with the dry ingredients. Mix just until combined after each addition. Do not overmix.

Divide the batter evenly between the prepared pans.

Bake for 18–24 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs.

Allow the cakes to cool in the pans for 10 minutes before transferring them to a wire rack to cool completely. For the easiest assembly, wrap the cooled cake layers tightly in plastic wrap and freeze for at least 1 hour or until firm.

Combine the strawberries, blueberries, raspberries, blackberries, sugar, lemon juice, and vanilla bean paste in a medium bowl.

Let the berries sit for 20 to 30 minutes, stirring occasionally.

Strain the berries, reserving the syrup to brush the cake layers.

In the bowl of a stand mixer fitted with the paddle attachment, beat together the cream cheese and mascarpone until smooth. Add in powdered sugar, vanilla bean paste, and almond extract until smooth again.

Switch to the whisk attachment. With the mixer on low speed, slowly pour in the cold heavy cream.

Increase to medium-high speed and whip until medium-stiff peaks form. The frosting should be fluffy and hold its shape without becoming grainy.

If needed, level the tops of the cake layers. Place one cake layer on a cake stand or serving plate.

Lightly brush the cake with about 1 tablespoon of the reserved berry syrup.

Spread about 1¼ cups of Chantilly frosting evenly over the cake.

Pipe a frosting border around the edge.

Spread half of the drained berries inside the border.

Repeat with the second cake layer.

Top with the final cake layer, then apply a thin crumb coat and refrigerate for 20 minutes.

Finish frosting the cake with the remaining Chantilly frosting and decorate with fresh berries. If the cake is cold, allow it to sit for 20 minutes before serving and enjoying.