Preheat the oven to 350°F.
Liberally grease and flour a bundt pan - set aside.
Cream the butter and sugar together in a large bowl until light and fluffy.
Mix in the eggs one at a time - be sure to beat well after each addition.
Stir in the lemon zest, lemon juice, and vanilla extract.
Whisk the flour, baking powder, baking soda, and salt in a separate bowl, then add it to the batter in alternating additions with the buttermilk. Mix until just combined
Toss the blackberries with the tablespoon of flour and then gently fold them into the batter.
Transfer the batter to the prepared pan and smooth the top
Bake for 50–60 minutes, or until a toothpick inserted comes out clean. You can also gently press the center of the cake; if it springs back, it is likely done. However, this method is less reliable with bundt cakes because they are so thick.
Cool the cake in the pan for 10–15 minutes before turning it out onto a wire rack to cool completely.
While the cake is cooling, create the glaze by whisking the confectioner’s sugar, lemon juice, and zest in a small bowl until smooth.
Drizzle the glaze over the cooled cake before serving.
Garnish with additional lemon zest, if desired.