Preheat the oven to 350 degrees F (175 degrees C). Grease and flour two 8-inch round cake pans.

Sift cake flour, sugar, 1/2 cup cocoa powder, baking powder, and salt together in the bowl of a stand mixer fitted with a paddle attachment. Add 1 stick butter and oil and beat on slow speed for 1 to 2 minutes. Increase speed to high for 4 minutes. Turn off mixer and scrape sides of the bowl. Add 1 cup milk, eggs, applesauce, and chocolate extract and beat on medium speed until well combined into a thick batter. Pour evenly into the prepared cake pans.

Bake in the preheated oven until a toothpick comes out clean and the center springs back to a light touch, 25 to 35 minutes. Allow to cool completely, about 30 minutes. Slice each cake in half horizontally to create 4 layers.

Combine semi-sweet chocolate chips and bittersweet chocolate chips in the top of a double boiler set over hot but not boiling water. Stir until chocolate is melted and smooth, about 5 minutes. Remove from heat and let sit.

Cream 2 sticks butter in the bowl of the stand mixer. Mix on low speed and add confectioners' sugar, 8 tablespoons milk, 1 tablespoon chocolate extract, and 1 teaspoon cocoa. Scrape the bowl and add melted chocolate chips. Mix frosting until fluffy and light.

Pour raspberry preserves in a microwave-safe bowl and warm in the microwave oven for 1 minute; stir well.

Place the first cake layer on a serving plate and spread 1/2 the jar of preserves just to the edge. Lay the second layer on top and spread about 1 cup of frosting just to the edge. Lay the third layer down and spread remaining preserves just to the edge. Lay the final layer down and frost the entire cake with a thin crumb-coating of frosting, reserving remaining frosting. Refrigerate cake for 30 minutes.

Remove cake from refrigerator and decorate as desired with remaining frosting.