For the cake: Place an oven rack in the center of the oven and preheat it to 350°F. Spray 3 (8-inch) round cake pans with baking spray and line the bottoms with parchment paper.

In a medium bowl, whisk together the flour, cornstarch, baking powder, and salt. Set aside.

In a stand mixer fitted with the paddle attachment, beat the butter and granulated sugar on medium-high speed until light and fluffy, about 3 minutes. Reduce the speed to low and stream in the oil. Increase the speed to medium-high and beat until smooth, about 1 minute.

Beat in the eggs and egg whites, one at a time, on medium-low speed, scraping the bowl as needed. Beat in the vanilla and almond extracts. Reduce the mixer speed to low and gradually beat in the flour mixture in three batches, alternating with the buttermilk. Beat until just incorporated.

Divide the batter evenly among the prepared pans. Bake, rotating the pans halfway through, until the cakes are golden around the edges and a toothpick inserted into the centers comes out clean, 35 to 40 minutes. Transfer to cooling racks and let the cakes cool in the pans for 10 minutes. Remove the cakes from the pans, peel off the parchment rounds, and return the cakes to the racks to cool completely, about 1 hour.

For the frosting: In the bowl of a stand mixer fitted with the whisk attachment, whip the cream cheese, mascarpone, powdered sugar, and salt on medium-high speed until smooth and fluffy, 3 to 4 minutes. Reduce the speed to medium and gradually add the heavy whipping cream and vanilla, whipping until well combined and stiff peaks form, 1 to 2 minutes, stopping occasionally to scrape the sides of the bowl.

For the filling: In a small bowl, whisk together the raspberry jam and 3 tablespoons hot water to thin the jam; set aside. In a medium bowl, combine the blackberries, blueberries, raspberries, and sliced strawberries.

Trim the tops of the cakes with a long serrated knife to make them level, if necessary. Spread 1 tablespoon of the frosting on a cake stand or platter (to keep the cake from sliding while you decorate) and place 1 cake layer on top. Brush the top of the cake layer fully with some of the raspberry syrup. Spread with 1 cup frosting and sprinkle with 1 ¼ cups berries. Repeat with a second layer of cake, raspberry syrup, another cup of frosting, and 1 ¼ cups berries. Top with the remaining cake round, cut-side down.

Spread the remaining frosting over the top and sides of the cake. Smooth out the top and sides using a bench scraper, offset spatula, or butter knife held at an angle. Use an offset spatula or butter knife to create diagonal swipes up the sides for a textured design. Arrange the remaining berries and halved strawberries in a crescent shape on the top of the cake along one edge. To make the berries glossy, brush them with apricot jam, if you like.