Preheat your oven to 350F. Prepare your pan by lining with cupcake liners and set aside.
In a medium-sized bowl, sift 1 1/4 cups flour, 1 1/2 teaspoons baking powder and 1/4 teaspoon salt. Set aside.
Using a handheld electric mixer or a stand mixer fitted with the paddle attachment, beat the 6 tablespoons butter and 3/4 cup sugar on medium-high speed until light and fluffy.
Switch to low speed and add the egg. Once incorporated well, add the egg white. Then add the 1 teaspoon vanilla.
Still on low speed, add a third of your flour mixture then half of your milk. Add another third of your flour, the rest of your milk and finally the rest of your flour. Do not over-beat; just mix until each addition is incorporated and no significant traces of flour can be seen. Remember to scrape the bottom and sides of your bowl.
Scoop the batter into your cupcake liners (about 3/4 full) and bake for 18-20 minutes or until a toothpick inserted in the centre comes out clean.
Take out of the oven and let cool in the pan on a wire rack for about 5 minutes. Then take out of the pan and cool the cupcakes on the wire rack completely.