With a wooden spoon, beat the butter and sugar together in a large bowl until well-combined.
In a large bowl, whisk together the flour, baking powder, baking soda, and salt.
In a medium bowl, whisk together the eggs, egg yolk, buttermilk, and vanilla.
Alternate adding the dry and wet ingredients to the butter mixture alternately, in 2 or 3 additions each. Mix until just combined.
Fold in the blueberries. Pour the mixture into a lightly greased 9- by 9-inch cake pan, then bake in a 350° F oven until a toothpick inserted into the center comes out clean, 20 to 30 minutes. Cool completely, then cut into 8 bars.
To make the glaze, whisk the powdered sugar, buttermilk, and milk together to combine. Make sure the glaze is runny. Add additional milk, 1 tablespoon at a time, if needed.
Place the bars on a wire rack and pour the glaze over top. Letit set completely before serving.
I always carry three kinds of hot sauce in my purse. I have a soft spot for making people their favorite dessert, especially if it's pie. My first cookbook, The Fearless Baker, is out on October 24, 2017.