Position a rack in the center of the oven and heat the oven to 350 degrees F. Coat a 9x9x2 straight sided square cake pan (10 cup volume minimum) with the butter and lightly dust with the granulated sugar. Do not use a smaller pan or you will have a big but very tasty mess in your oven.
In a small bowl, stir the oil, molasses and eggs until combined. In a large bowl, whisk the flour, baking soda, ginger, cinnamon and salt.
In a small pot, bring the brown sugar and root beer to a boil. Meanwhile, add the molasses mixture to the flour and stir to combine. Add the hot root beer mixture and quickly beat until combined.
Pour the batter into the prepared pan and bake until a toothpick inserted in the center of the cake comes out clean (35-45 minutes). Let cool in the pan on a wire rack until warm (40 minutes).
Invert the pan to remove the cake and turn the cake right side up (cake may be prepared up to 4 hours ahead).
In a chilled medium bowl, beat the cream and sugar with a hand mixer until soft peaks form (3 minutes). Cut the gingerbread into 8 pieces of whatever size you choose and place one on each of 8 plates. Top with a dollop of whipped cream and serve.
Cupcakes: (20 cupcakes) Fill each just a bit above halfway. Bake trays at 350 degrees F for 19 minutes (rotate & switch midway).