Preheat your oven to 350 degrees F. Line a muffin tin with cupcake liners.
In a small bowl, whisk together the sifted all-purpose flour, baking powder, ground ginger, cinnamon, ground cardamom, ground cloves, ground allspice, freshly ground nutmeg, and salt. Set it aside.
Add the unsalted butter to the bowl of an electric mixer and beat it until creamy. Add the granulated sugar and beat with the butter on high speed until fluffy.
Add in the large egg and egg white, mixing well on medium speed until combined.
Add in the vegetable oil and vanilla extract, beating on medium speed for another minute.
With the mixer on low speed, add in half of the dry ingredients. Pour in the whole milk and add in the other half of the dry ingredients, mixing until just combined.
Fill the cupcake liners about three-quarters full with batter. Bake until the tops are set, about 16 to 17 minutes.
Let cool completely before frosting.
In a clean mixing bowl, add the unsalted butter for frosting and beat on high speed until creamy.
With the mixer on low speed, slowly add in the powdered sugar, followed by the spices and vanilla extract.
Beat until fluffy and creamy. If the frosting seems too thick, add a tablespoon of milk.
Frost the cupcakes once cooled. To make the crunchy sugar topping, stir together the raw sugar with the spices and sprinkle on top.