Preheat your oven to 350°F (175°C). Grease and flour a bundt pan thoroughly.
In a large bowl, cream together the softened butter and sugar until the mixture is light and fluffy. Add the eggs one at a time, making sure to beat well after each addition. Stir in the vanilla extract.
In a separate bowl, whisk together the flour, baking powder, baking soda, and salt. Gradually add this dry mixture to the butter mixture, alternating with sour cream. Beat well after each addition until the batter is smooth.
Spoon one-third of the batter into the prepared bundt pan.
For the filling, combine the brown sugar, flour, and cinnamon in a small bowl. Sprinkle half of this mixture over the batter in the pan, then top with half of the fresh blueberries.
Add another layer of batter, followed by the remaining brown sugar mixture and blueberries. Top with the remaining batter.
Bake in the preheated oven for 55-65 minutes, or until a toothpick inserted into the center of the cake comes out clean. Let the cake cool in the pan for 10 minutes before carefully inverting it onto a wire rack to cool completely.
Once the cake has cooled slightly, prepare the glaze by whisking together the powdered sugar and milk. Drizzle the glaze over the warm coffee cake and allow it to set.