Preheat your oven to 350°F (175°C). Grease and flour a 9-inch round cake pan to prevent sticking.

In a mixing bowl, cream together the softened butter and 3/4 cup of granulated sugar using an electric mixer on medium speed until light and fluffy, about 3-5 minutes. This incorporates air into the batter, helping the cake rise.

Add the eggs one at a time, mixing well after each addition. This ensures even distribution of the eggs throughout the batter.

Stir in the buttermilk and vanilla extract until well combined.

In another bowl, whisk together the sifted flour, baking powder, baking soda, and salt. Gradually add this dry mixture to the wet ingredients, mixing just until combined. Be careful not to overmix, as this can lead to a dense cake.

Gently fold in the blackberries using a rubber spatula, being careful not to break them up too much.

Pour the batter into the prepared cake pan and smooth the top with the spatula.

Bake in the preheated oven for 30-40 minutes, or until a toothpick inserted into the center comes out clean. This ensures the cake is fully cooked.

Once baked, remove from the oven and let the cake cool in the pan for 10 minutes before transferring it to a wire rack to cool completely.

In a small bowl, whisk together the sifted powdered sugar, milk, and vanilla extract until smooth. Adjust the milk quantity as needed to achieve your desired glaze consistency.

Once the cake has cooled completely, drizzle the glaze over the top of the cake, allowing it to drip down the sides for a beautiful presentation.