Preheat oven to 325°F. Grease three 8" cake pans and set aside (see note).
In the bowl of a stand mixer, combine butter, coconut oil, sugar, baking powder, baking soda, and salt. Mix until light and fluffy. Scrape down the sides of the bowl.
With the mixer running on low, add the egg whites one at a time. Add vanilla bean paste (see note) and mix to combine.
With the mixer running on low, alternate additions of flour and buttermilk. Add ⅓ of the flour, followed by ⅓ of the buttermilk. Repeat for remaining flour and buttermilk, allowing each addition to incorporate before adding the next.
Divide the batter between the prepared pans (see note). Affix cake strips, if using (see note).
Bake for about 40 minutes, turning the cakes around at the halfway point to help ensure an even bake. A toothpick inserted in the center of the cake should come out clean. Allow the cakes to cool completely on a wire rack.
For Blackberry Reduction:
Combine blackberries, sugar, and lime juice in a medium saucepan. Over medium heat, cook mixture until juices bubble and berries are soft.
Using a fine mesh strainer, strain the mixture, discarding the seeds and pulp. Return the juice to the pan.
Over medium heat, cook blackberry juice until reduced to about 2 tablespoons, about 10 minutes. Let cool completely.
For Buttercream:
Combine egg whites and sugar in the bowl of a stand mixer and whisk to combine. Place the bowl over a pan of simmering water, taking care that the water doesn't touch the bowl. Cook mixture on medium heat until it reaches 160°F.
Once the mixture reaches temperature, carefully transfer the bowl to the mixer. Using the whisk attachment, beat on high speed until white, glossy, and bowl is no longer warm to the touch, about 10 minutes.
With the mixer running on low speed, add butter a few pieces at a time. Allow each addition to incorporate before adding the next. Once all butter is incorporated, add vanilla extract and whip until smooth, another 3-5 minutes.
Add blackberry reduction and whip until fully combined.
Frost the cooled cakes with buttercream. Top with fresh blackberries, if desired.Enjoy!
Notes
Note on cake flour and coconut oil: These ingredients help lend the cake it's super soft and fluffy texture. I don't suggest substitutions for these!Note on buttermilk: If you don't have buttermilk, you can make a quick substitution with milk (2% milkfat or greater) and vinegar or lemon juice. For this recipe, pour 2 tablespoons lemon juice or vinegar into a liquid measure, then add enough milk to come up to the 2 cup line. Let sit for 5 minutes, then it's ready for use!Note on vanilla bean paste: You know me, it's in everything! Delicious and more economical than whole vanilla beans, this ingredient is my go-to for an extra punch of flavor. You can find it online [here]. If you prefer to substitute, you can use an equal measure of vanilla extract.Note on cake pans: This recipe is for an 8" triple-layer cake. If you don't have three pans, the batter will still be good at room temperature for about three hours if you need to bake them individually. See note on using a kitchen scale--it's much easier to divide the batter equally when you have one!Also...I've made this recipe in both 8" pans and 6" pans. If you prefer to make an 6" triple-layer cake, make half the cake recipe as written here. Bake time will be about 30 minutes. You'll need about ⅔ this buttercream recipe for a 6" cake. If you're looking to get some 6" pans for yourself, these are the ones that I use [here]. Note on kitchen scale: To ensure I have the same amount of batter in each pan, I use my kitchen scale (link [here]) and weigh the pans. It's hard to eyeball the amount when you're using three pans, especially if you don't have three and you're baking the cake layers individually.Note on cake strips: I use cake strips on my pans when making a layer cake, since they help the cake bake up flatter (see: easier assembly). If you’re in the market for them, you can find them [here].