In a large bowl using a handheld or stand mixer fitted with a paddle attachment, beat the butter and brown sugar together on medium speed until creamy. Beat in the egg until combined, scraping down the sides and bottom of the bowl as needed. Beat in the milk, molasses, and vanilla on medium speed. Mixture will be piecey and not fully combined. That's ok.
In a medium bowl, toss the flour, baking powder, baking soda, salt, cinnamon, ginger, nutmeg, and allspice together until combined. With the mixer running on low speed, slowly pour the dry ingredients into the wet ingredients. Mix until just combined. Scrape down the sides and bottom of the bowl as needed.
Fill cupcake liners 2/3 of the way full, no more. Bake for 19-21 minutes or until a toothpick inserted in the center comes out mostly clean. Allow to cool completely before frosting.
Mix together butter and powdered sugar in a standing mixer. Add vanilla and 1/3 of cream and mix. Add more cream until you get a stiff buttercream. Place in a piping bag with desired tip.
Place ingredients into saucepan over medium heat. When sugar as dissolved remove from heat and let cool. Place in refrigerator overnight. When ready to serve roll in fine white sugar.