Preheat oven to 350F (175C) and line a 12-count muffin tin with paper liners.
In a large mixing bowl, whisk together flour, brown sugar, baking soda, baking powder, salt, and spices (ginger, cinnamon, nutmeg, allspice, cloves).
Add melted butter and oil and stir well. Batter may be a bit dry, but make sure all of the flour is moistened.
Add molasses and stir well.
Stir in egg, egg yolk, and vanilla extract until thoroughly combined.
Add hot water and stir again until batter is completely combined, then stir in sour cream until batter is uniform (make sure to scrape sides and bottom of the bowl).
Divide batter evenly into prepared cupcake pan (filling liners approximately ¾ full) and bake in center rack of 350F (175C) oven for 18 minutes or until a toothpick inserted in the center comes out clean or with moist crumbs. Allow cupcakes to cool in pan for 10-15 minutes before carefully removing to a cooling rack and allowing to cool completely before frosting.
In a large mixing bowl, combine cream cheese, butter, brown sugar, vanilla bean paste (or vanilla extract), cinnamon, and salt. Use an electric mixer to stir together until smooth, creamy, and well-combined,
With mixer on low-speed, gradually add powdered sugar until completely incorporated and frosting is smooth and creamy.
Spread or pipe over cooled cupcakes. I like to use an Ateco 848 or Ateco 846 tip. This frosting makes enough to generously cover each cupcake (as shown in the photos).