Preheat your oven to 350°F (175°C). Grease and flour a 9-inch round cake pan.
In a mixing bowl, cream together the butter and sugar until light and fluffy. Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
In another bowl, whisk together the flour, baking powder, and salt. Gradually add the dry ingredients to the creamed mixture alternately with the milk, beginning and ending with the dry ingredients. Fold in the blueberries.
Pour the batter into the prepared cake pan. Bake for 45 minutes or until a toothpick inserted into the center comes out clean. Allow the cake to cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.
Notes:
For a little extra flavor, you can add a teaspoon of lemon zest to the batter.