Preheat your oven to 350°F (175°C). Grease and flour a 9-inch (23cm) round cake pan or line it with parchment paper.
In a medium bowl, whisk together the sifted all-purpose flour, baking powder, and salt. Set aside.
In a large mixing bowl, beat the softened unsalted butter and 1 3/4 cups granulated sugar 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 1 tablespoon vanilla extract.
Alternately add the dry flour mixture and 1 cup whole milk to the butter mixture, beginning and ending with the flour mixture. Mix each addition just until combined; do not overmix.
In a small bowl, combine 1/4 cup granulated sugar, cornstarch, 1/2 teaspoon vanilla extract, and 2 tablespoons whole milk to create the vanilla swirl mixture. Stir until smooth.
Pour half of the cake batter into the prepared cake pan. Spoon half of the vanilla swirl mixture evenly over the batter. Use a knife or skewer to gently swirl the vanilla mixture into the batter to create a marbled effect.
Pour the remaining cake batter over the swirled layer, then spoon the remaining vanilla swirl mixture on top. Swirl again gently with a knife or skewer.
Bake in the preheated oven for 38-42 minutes, or until a toothpick inserted in the center comes out clean.
Remove the cake from the oven and allow it to cool in the pan for 10 minutes. Then transfer the cake to a wire rack to cool completely before slicing and serving.