Preheat the oven to 325°F and grease and flour two 8 or 9 inch cake pans (or 3 6 inch cake pans like we have here). Set aside.
In a large mixing bowl fitted with a whisk attachment, beat the softened butter and oil together until they become homogenous, about 3 minutes. This will not work if your butter is not completely room temperature.
Slowly add the granulated sugar to the oil and butter, beating on high until the mixture is light and fluffy and turns a very pale yellow, about 3 minutes.
Add the eggs in one at time, scraping down the bowl in between each addition. Add the vanilla extract. Beat the mixture on high for 3 minutes more to incorporate as much air as possible.
In separate bowl sift together the cake flour, salt, and baking powder. Alternate mixing in the dry ingredients and the buttermilk in 4 batches, starting with the buttermilk and ending with the dry ingredients. It’s okay if the batter still has a few lumps in it–you don’t want to over mix it.
Split the batter evenly into the prepared pans and bake for 30 minutes or until the cake is a lightly golden brown and springs back when pressed. This will depend on your oven. Take out of the oven and transfer to a cooling rack until the pans are cool enough to touch. Once cool, turn the cakes out of their pans, peel off the parchment and allow to cool completely before frosting.
Once the cakes are cool, make the cream cheese frosting. Place the softened butter and cream cheese in a stand mixer fit with the whisk attachment. Beat the butter and cream cheese together until homogenous and fluffy, about 2 minutes.
Add the vanilla extract, salt, and powdered sugar and whip to combine. After about a minute of mixing, use a rubber spatula to scrape down the bowl and beat for 2 more minutes until light and fluffy. Transfer to a large piping bag to make frosting easier!
Place your first cake layer on your cake stand or serving dish. Pipe a circle of frosting around the outer edge of the top of the cake. In a random pattern, pipe frosting into middle of cake, then smooth out middle of frosting with a spatula, keeping the edge/outer rim of the frosting intact. (Basically you’re making a super shallow divot for the jam). Fill inner divot with 1/3 cup blackberry jam, spreading it evenly.
Repeat with second layer. For third layer, frost top of cake normally, then frost outside with remaining frosting.
If desired, top with blackberries and edible flowers! Refrigerate until ready to serve!