Preheat the oven to 350°F (175°C). Spray two 8-inch cake pans with nonstick baking spray, line their bottoms with parchment paper rounds, and spray the parchment.

Sift the flour into a medium bowl. Whisk in the baking powder, baking soda, and salt, then set the mixture aside.

Using a mixer, beat the butter, oil, and granulated sugar on high speed for about 3 minutes, until light and fluffy. Mix in the sour cream and vanilla.

Add the eggs one at a time, mixing on medium speed after each addition until incorporated.

With the mixer on low, add one-third of the dry ingredients, followed by half of the buttermilk. Add another third of the dry ingredients and the remaining buttermilk, then mix in the final third of the dry ingredients just until combined.

Divide the batter evenly between the prepared cake pans and smooth the tops.

Bake for 27–30 minutes, or until a toothpick inserted in the center comes out clean. Let the cakes rest in their pans for 10 minutes, then turn them out onto a cooling rack and cool completely.

While the cakes cool, combine the raspberries, sugar, lemon juice, and salt in a medium saucepan over medium heat. Cook until the berries soften, then mash them.

Press the mashed berries through a fine-mesh sieve and discard the seeds. Return the strained mixture to the saucepan, stir in the cornstarch, and cook until thickened. Transfer the jam to a bowl and cool completely.

Let the butter sit at room temperature for about 30 minutes so it is slightly softened but still cool. Sift the powdered sugar into a large bowl. Grind the freeze-dried raspberries in a food processor, then stir the powder into the powdered sugar.

Beat the cream cheese and butter on high speed for 3 minutes. Add the powdered sugar and ground raspberries and mix until combined. The frosting will be thick. Add the vanilla, salt, and heavy cream, then beat on high until smooth and spreadable.

Use a serrated knife to trim the domed tops from the completely cooled cake layers. Secure the first layer to a cake board or serving plate with a small dab of frosting.

Spread about 1 cup of frosting over the first cake layer. Pipe a border of frosting around the edge to contain the filling, then spread the cooled raspberry jam inside the border.

Place the second cake layer on top with its flat bottom facing up. Spread a thin crumb coat of frosting over the cake and freeze for 15 minutes.

Cover the chilled cake with the remaining frosting and decorate with fresh raspberries. Freeze for another 15 minutes before serving so the frosting can set.