In the mixing bowl of a stand mixer, place the softened butter, brown sugar, and sugar, and whisk until smooth.
Add the eggs, vanilla, molasses, heavy cream and mix on medium speed until smooth, and blended.
Turn mixer to high for about 30 seconds, and blend.
In a separate bowl, mix the flour, baking powder, baking soda, salt, cinnamon, ginger, nutmeg, and allspice, until well blended.
Add the flour mixture to the mixing bowl, a little at a time, mixing between additions until all ingredients are mixed and blended smooth.
Scrape down the sides of the bowl, and fold any remaining or unmixed ingredients into the batter.
Line cupcake pans with cupcake liners and Fill the cupcake liners 2/3 full.
Bake at 350 for 20 - 25 minutes, or until a toothpick inserted in the center comes out clean.
Remove from the oven to a wire rack to cool completely.
While the cupcakes are cooling; rinse out the mixing bowl, and add the softened cream cheese, and mix with the whisk attachment until smooth and creamy.
Add the heavy cream and brown sugar, and blend until smooth. Add the vanilla, cinnamon, and allspice, and mix.
Add the powdered sugar in thirds, and blend well between additions, until all the powdered sugar is added to the cream cheese mixture, and the Frosting is smooth and creamy.
Frosting should be thick, if it's not thick, add a little more powdered sugar. If you think it's too thick, add a little cream, a few drops at a time until you get the right consistency.
Place the frosting in the refrigerator until the cupcakes are completely cool.
When the cupcakes have cooled, remove the frosting from the refrigerator, and place the frosting in a pastry bag with a large tip (see link).
Pipe the frosting onto the cupcakes, starting at the outer edge, and working around, swirling up to a point in the center.
Continue adding frosting to the bag, and frosting the cupcakes until all cupcakes have been frosted.
Sprinkle with Gingerbread cookie crumbs or colored icing sugars.
Serve and Enjoy!