Preheat oven to 350 °F (177 °C) and grease and flour a 12-cup bundt pan. Set aside.
In a medium bowl, whisk together flour, baking powder, and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter, sugar, and vegetable oil together on medium speed, until light and fluffy, about 5 minutes. Reduce speed to low and beat in the eggs, one at a time, then beat in the vanilla. Add about one-third of the flour mixture and half of the buttermilk; beat until almost incorporated. Add another one-third of the flour mixture and the remaining buttermilk. Beat, scrape down the sides of the bowl as needed, and then add the remaining flour mixture and beat about 30 seconds. Finish incorporating the flour by hand to avoid overmixing.
Toss the blueberries with the remaining 2 tablespoons of flour in a small bowl. Spoon one-third of the batter evenly into the prepared pan, Sprinkle in half of the blueberries, then top with another one-third of the batter. Scatter the remaining blueberries on top and cover with the rest of the batter and smooth out the top.
Bake until cake is golden brown and toothpick inserted into the center comes out clean, about 1 hour to 1 hour and 10 minutes.
Transfer to a rack and let cool 30 minutes in the pan. Run a small sharp knife along the edge of the pan to loosen the cake then invert onto the rack to cool completely.
Meanwhile, make the glaze. Whisk the confectioners sugar, butter, and 4 tablespoons of milk together in a bowl. If the glaze is too thick, whisk in one more tablespoon of milk, a little at a time.
Once cake has cooled, transfer to a cake stand (or whatever you want to serve it on), pour the glaze over the cake and let it drip down the sides. Slice and serve.
Store in an airtight container for up to one week.