Step 1
Preheat the oven to 350 degrees F (175 degrees C). Line the bottom of two 8-inch round cake pans with parchment paper. Place a mixing bowl and beaters into a refrigerator to chill for whipped cream frosting.
Step 2
Whisk flour baking powder baking soda and salt together in a bowl.
Step 3
Combine sugar and butter in the bowl of an electric stand mixer and beat at medium speed until mixture is creamy and smooth 5 to 10 minutes. Meanwhile beat eggs in another bowl until foamy.
Step 4
Slowly add beaten eggs to the bowl of the stand mixer and reduce speed to low. Add dry ingredients in small increments alternating with buttermilk until just combined. Add lime zest and juice and mix just until combined. Pour 1/2 of the batter into each prepared cake pan.
Step 5
Bake in the preheated oven until a toothpick inserted into the center of the cakes comes out clean 15 to 20 minutes. Let cool completely in the pans on wire racks before removing about 30 minutes.
Step 6
While cakes are cooling make the curd. Add sugar butter lime juice and zest to the top of a double boiler filled with at least 1 inch of water in the bottom. Set heat to medium and mix until butter melts. Add 2 tablespoons of the mixture to the beaten eggs and stir until combined. Reduce heat on the double boiler until water is simmering; add eggs and mix until curd coats the back of a wooden spoon 20 to 25 minutes.
Step 7
Let curd cool slightly about 10 minutes. Transfer to a glass container and refrigerate until needed.
Step 8
For the frosting combine blackberries and lime juice in a small saucepan over medium heat. Cook and stir for 20 minutes. Strain the mixture; if less than 3 tablespoons of liquid results add small amounts of water to the pulp until 3 tablespoons is achieved. Allow juice to cool to room temperature about 10 minutes.
Step 9
Pour blackberry juice and butter into a mixing bowl and beat until creamy. Slowly add powdered sugar and vanilla extract and beat to a thick consistency. Add milk and beat until combined.
Step 9
Remove chilled mixing bowl and beaters from the refrigerator. Add heavy cream and beat until cream is frothy. Slowly add powdered sugar and vanilla extract while beating; beat until frosting can hold stiff peaks.