Bring eggs, buttermilk, and 1 cup plus 2 tbsp of butter to room temperature.
Preheat the oven to 350°F.
Sift together the flour, baking powder, salt, and baking soda in a medium-sized bowl and set aside.
Using a stand or hand mixer, cream together butter, granulated sugar, and vanilla. Beat until very creamy. Then add the eggs one at a time, beating well after each addition.
Mix together the lemon juice, lemon zest, and buttermilk. Add to the butter/sugar mixture alternately with the sifted dry ingredients. Beat until fully combined and all of the dry ingredients are fully moistened.
Grease a Great Bundt pan with non-stick cooking spray or use “cake goop.” *see notes
Pour 1/3 of the batter into the pan. Place a 1/4 cup of blueberries on top of the batter. Keep them from touching the sides of the pan. Pour another 1/3 of the batter, and again carefully place 1/4 cup of blueberries, keeping the berries in the center. Put the remaining batter in, ending with the remainder of the blueberries. Using this layering method will help prevent the blueberries from sticking to the pan.
Bake for 50-60 minutes or until a toothpick inserted comes out clean.
Allow the cake to cool for 5 minutes right side up; then for another 5 minutes upside down on a cooling rack. The cake may drop out of the pan as soon as you turn the pan onto the rack. If it has not dropped out of the pan onto the rack, give it a few gentle side-to-side jiggles. That is often enough to release the cake from the pan.
Allow the cake to completely cool, about 1 hour.
For the glaze: In a medium bowl, mix powdered sugar, butter, vanilla, and 4 tbsp spoons of milk until smooth. Add additional milk until you reach the desired consistency.
Drizzle the glaze over the cake.