Preheat the oven to 350°F (175°C). Grease and flour a 9-inch (23cm) round cake pan.
In a medium bowl, whisk together the all-purpose flour, baking powder, and salt. Set aside.
In a large bowl, beat the softened butter and 1 1/2 cups granulated sugar together until light and fluffy, about 3-4 minutes.
Add the eggs one at a time, beating well after each addition.
Mix in 1 tablespoon vanilla extract.
Alternately add the flour mixture and whole milk to the butter mixture, beginning and ending with the flour mixture. Mix until just combined.
In a small bowl, combine 1/4 cup granulated sugar and 1 tablespoon vanilla extract to create the vanilla swirl mixture.
Pour half of the cake batter into the prepared pan.
Drop spoonfuls of the vanilla swirl mixture over the batter in the pan.
Pour the remaining cake batter over the swirl mixture.
Using a knife or skewer, gently swirl the batter to create a marbled effect, being careful not to overmix.
Bake for 38-40 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 before serving.