Preheat the oven to 350 degrees F (175 degrees C). Grease and flour an 8x8 inch or 9x13 inch baking pan.
In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
In a large bowl, cream together the butter and granulated sugar until light and fluffy.
Beat in the eggs one at a time, mixing well after each addition.
Stir in the lemon zest, milk, and vanilla extract.
Alternate between adding the dry ingredients and the milk to the wet ingredients, beginning and ending with the dry ingredients. Blend until just combined – don't overmix!
Gently fold in the blueberries.
Pour the batter into your prepared pan and spread evenly.
Bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan completely before glazing.
Make the lemon glaze:
Whisk together the powdered sugar and lemon juice. Start with 2 tablespoons of lemon juice, and add more until you reach your desired consistency.
Drizzle the glaze over the completely cooled cake.
Notes
Use fresh lemons for the best lemon flavor.
For an extra lemon flavor, add a teaspoon of lemon juice to the cake batter.
Don't over bake the cake! Start checking on it at the 30 minute mark.