1. Preheat the oven to 375 degrees, and grease a 9x13 baking dish.
2. Combine the flour, baking powder and salt together in a bowl together; set aside.
3. In your stand mixer, beat the 1/3 cup butter and 2 tablespoons sugar together.
4. Combine eggs and vanilla with the butter and sugar.
5. Mix in the dry ingredients and milk until it is well combined.
6. Pour the cake batter into the greased 9x13 baking dish and spread batter evenly in the baking dish.
7. To the baking dish, add the 4 cups of black raspberries on top of the cake batter. Spread as evenly as possible over the top of the cake batter. The berries will completely cover the top of the batter.
8. Bake for 35 minutes.
9. To test if the black raspberry cake is done when the timer goes off, insert a toothpick into the center of the cake. If the toothpick comes out with batter on it, leave the cake in for another few minutes and test again. When toothpick comes out clean from the black raspberry cake, take it out of the oven, let cool for 5-10 minutes in the baking dish before frosting.
10. Frosting: While it is cooling, prepare the frosting by mixing together the remaining 1 stick of butter and 2 cups powdered sugar. The frosting when done will be very thick.
11. Spread the frosting on the black raspberry cake by first putting spoonfuls of frosting around the baking dish on the cake itself. As the frosting sits on the warm cake, it will soften and can be spread with a knife to bring out the beautiful color of the black raspberries.
12. Serve while still warm and enjoy!