Preheat your oven to 375°F (190°C) and grease a 9-inch round cake pan.
In a medium bowl, whisk together the flour, baking powder, and salt until well combined.
In a large bowl, use an electric mixer to cream the softened butter and sugar together on medium speed for 2-to-3 minutes, until the mixture is light and fluffy.
Beat the egg and vanilla extract into the butter mixture until fully incorporated.
Gradually add the dry ingredients to the wet ingredients, alternating with the milk, and mix on low speed until the batter is just combined and no dry streaks of flour remain.
Gently fold the fresh blueberries into the batter using a spatula, being careful not to overmix.
Pour the batter into the prepared pan and bake for 25-to-30 minutes, or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan on a wire rack for at least 15 minutes before slicing and serving.