Preheat the oven to 350F. Line a cupcake pan with paper liners and set aside. Line a medium baking sheet with foil.
In a measuring cup, combine the egg, egg white, vanilla and oil. Whisk to combine.
1 large egg, room temperature, 1 large egg yolk, temperature, 2 teaspoons pure vanilla extract, 2 tablespoons canola oil
In the bowl of a mixer fitted with the paddle attachment, combine the cake flour, sugar, baking powder, salt, cinnamon and nutmeg and mix on low speed for a minute to combine.
1½ cups cake flour, ¾ cup granulated sugar, 2 teaspoons baking powder, ½ teaspoon fine sea salt, ¾ teaspoon cinnamon, ⅛ teaspoon nutmeg
With the mixer still running, add in the softened butter pieces. Mix on low speed until the mixture resembles coarse crumbs. You should be able to gather a bit in your hand, squeeze and you have a solid piece. This means the butter is evenly distributed.
5 tablespoons unsalted butter, room temperature
With the mixer still on low, slowly pour in the milk, mixing JUST until the flour mixture is moistened. You will not use all the milk at this time. Pour the remaining milk into the bowl with the eggs and oil, and whisk to combine.
½ cup whole milk, room temperature
Turn the mixer speed to medium and whip for a full 90 seconds. The mixture should be whipped up, thick, and lighter in color. Scrape the sides and bottom of the bowl to ensure everything is properly mixed.
With the mixer speed on low, add the egg/oil/remaining milk mixture in two additions, scraping down the bowl after each addition has been mixed in.
Once the remaining egg/oil mixture has been added, give the bowl a final scrape and mix with a spatula. Divide the batter among the 12 liners.
Bake the cupcakes for 17-20 minutes, until a toothpick comes out with a crumb or two when inserted in the center of the cupcake. Increase the oven temperature to 375F.
Place the baked cupcakes on wire racks to cool for 5 minutes. Carefully remove the hot cupcakes from the pan and cool completely on a wire rack.