Combine lime juice and cornstarch, to make a slurry, and mix until no lumps. Mix with blackberries and salt in a saucepan.
Use an immersion blender to make the filling smooth, turn on the heat, and being to cook down the berries, keep stirring to keep the puree from cooking too quickly on the bottom of the pan.
Once the puree has thickened up slightly, remove from heat stir in zest, and transfer to a bowl to cool to room temp. You will use about 6 Tablespoons of the puree to add to your cake, the rest will be used to color and flavor your buttercream.
You will end up with about 1/4-1/2 cup of puree for the buttercream. If you choose to strain the seeds out of all of the puree, add a couple of extra ounces of berries to account for the loss in straining.
I chose to leave the seeds in for the cake, and strain the seeds out for the buttercream, seeds can be left in for the buttercream too, your choice. Store leftover puree in the fridge for up to a week or freeze for 6 months.
Heat oven to 335º F/168º C. Prepare two 8″ round cake pans with cake goop or another pan release that you prefer.
Measure out the buttermilk. Place 4 oz in a separate measuring cup. Add the oil to the 4oz of buttermilk and set aside.
To the remaining milk, add your eggs, and lime zest, gently whisks to combine, and keep the lime juice separate, you will add this at the end.
Place the flour, sugar, baking soda, and salt into the bowl of your stand mixer with the paddle attachment. I’m using my Bosch universal plus mixer but you can use whatever mixer you have.
Turn the mixer onto the slowest speed (setting 1 on Kitchen Aid mixers). Slowly add chunks of your softened butter until it is all added then let everything mix until it looks like coarse sand.
Add your milk/oil mixture all at once to the dry ingredients and mix on medium (speed 4 on KitchenAid) for 1 full minute to develop the structure. Don’t worry, this will not over-mix the cake, because it is AP flour you do not need to mix as long as cake flour (more gluten, less time needed)
Scrape the bowl. This is an important step. If you skip it, you will have hard lumps of flour and unmixed ingredients in your batter. If you do it later, they will not mix in fully.
Slowly add in the rest of your milk/eggs/zest ingredients in 3 parts, and pour in the lime juice with the last addition of liquid, stopping to scrape the bowl one more time halfway through. Your batter should be thick and not too runny. Fill your pans 1/2 full with cake batter.
Spoon about 2 tablespoons of room temp puree over the batter, and use a small spatula or knife to gently fold the puree in to create a swirl effect into the batter.
Add floured blackberries to the top of the batter, do not push them down in as their weight will cause them to sink anyway as the cake heats up.
I always start by baking for 30 minutes for 6″ and 8″ cakes and 35 minutes for 9″ and larger cakes and then checking for doneness. If the cakes are still really jiggly, I add another 5 minutes. I check every 2 minutes after that until I’m close and then it’s every 1 minute. Cakes are done when a toothpick inserted in the center comes out with a few crumbs.
After the cakes have cooled for 10 minutes or the pans are cool enough to touch, flip the cakes over and remove them from the pans onto the cooling racks to cool completely. Wrap in plastic wrap and chill in the freezer.
Once the cakes are chilled in the freezer and feel firm you can trim off the brown edges from the sides (optional) and fill them with your blackberry buttercream and fresh berries. Crumb coat the cake with buttercream, chill then apply your final coat of buttercream. Top with fresh berries and lime zest.