Preheat the oven to 350°F (175°C). Grease and flour a 9×5-inch loaf pan or a 9-inch 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 3/4 cups granulated sugar together with an electric mixer on medium speed until light and fluffy, about 3 to 4 minutes.
Add the eggs one at a time, beating well after each addition. Stir in 1 tablespoon vanilla extract.
Alternately add the dry ingredients and the whole milk to the butter mixture, beginning and ending with the dry ingredients. Mix until just combined; do not overmix.
Remove about 1 cup of the batter and place it in a small bowl. Stir in the 1/4 cup granulated sugar and 1 tablespoon vanilla extract to create the vanilla swirl batter.
Pour the plain batter into the prepared pan. Drop spoonfuls of the vanilla swirl batter evenly over the top.
Using a knife or skewer, gently swirl the vanilla batter into the plain batter by making figure-eight motions to create a marbled effect.
Bake for 40 to 45 minutes or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan for 15 minutes, then transfer to a wire rack to cool completely before slicing and serving.