Preheat the oven to 350°F (175°C). Grease and flour a 9 x 13 inch baking pan and set aside.
In a medium bowl, whisk together 2 1/2 cups flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, beat the softened butter and granulated sugar together with an electric mixer on medium speed until light and fluffy, about 3-4 minutes.
Add the eggs one at a time, beating well after each addition.
Mix in the lemon zest, lemon juice, and vanilla extract until combined.
Add the dry ingredients to the wet ingredients in three additions, alternating with the sour cream, beginning and ending with the dry ingredients. Mix until just combined; do not overmix.
In a small bowl, toss the blueberries with 2 tablespoons of flour to coat them evenly. Gently fold the coated blueberries into the batter.
Pour the batter into the prepared 9 x 13 inch pan and spread evenly.
Bake for 40-45 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool completely in the pan on a wire rack.
In a small bowl, whisk together the powdered sugar, lemon juice, and lemon zest to make the glaze.
Once the cake is cooled, drizzle the lemon glaze evenly over the top.
Slice and serve.