Preheat oven to 350 degrees. Line a cupcake pan with paper liners.
In a large mixing bowl, add in butter, vegetable oil, brown sugar, and granulated sugar. Mix on medium until light and fluffy. It will take about 2 minutes to come together and cream.
Add in the molasses and mix until combined.
Add in the vanilla and the eggs one at a time. Once the first egg is completely incorporated, add in the second egg.
In a separate bowl, sift the ginger, cinnamon, nutmeg, clove, baking soda, baking powder, and cake flour.
Add a third of the flour and mix on low until combined.
Add half of the milk into the batter and mix until combined. Repeat with another third of flour, milk, and then a third of flour again. At this point, all of the flour and milk should be incorporated.
Scoop into the paper liners and give it a tap on the counter. Place into the oven for 22 to 24 minutes or until done. To check to see if the cupcakes are done, place a toothpick into the center of a cupcake. If it comes out clean or with a few moist crumbs on it, it's done. If it has raw batter, it still needs a few minutes. Be sure to not open the door too soon otherwise the cupcakes may fall.
Let the cupcakes completely cool. Then frost and decorate.
Frosting
In a double boiler, add in the butter and white chocolate chips. If you don't have a double boiler, add enough water to cover the bottom of a saucepan. Bring it to a simmer and add a heatproof bowl that sits on top of the saucepan to it. Make sure the water isn't touching the bottom of the bowl and that there is always water in the saucepan.
Whisk the butter and white chocolate chips until they are completely melted.
Once the butter and white chocolate chips are melted, remove from the heat and let cool for 10 minutes. Instead of waiting 10 minutes, I placed mine on a stand mixer and whipped it with the whisk attachment until it cooled down. If using a hand mixer, after the 10 minutes cooling, beat on medium for 1 minute.
Add in the powdered sugar and mix on low until combined. If it becomes too thick, add in the tablespoon of milk. If it's still not to your desired consistency, add the milk by the ½ tablespoon until it is. Whip an additional minute or two until the frosting becomes light and fluffy.
Place in a piping back with a 1M tip and pipe beautiful swirls on the cooled cupcakes. Sift a very small amount of the cinnamon through a very fine mesh sifter to get a dusting on your cupcakes. If you dump the whole teaspoon through the sifter, it's going to be a ginormous mess. Don't do that! Just sprinkle. Then add a few sprinkles to the tops.