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In a large Dutch oven, bring 3 inches oil to 375 degrees F. In the bowl of a stand mixer fitted with the paddle attachment, mix together the flour, granulated sugar, butter, baking powder, salt, allspice, cinnamon, cloves and ginger on low speed until the mixture looks like coarse sand, 3 minutes.
Whisk together the egg, vanilla and 3/4 cup root beer until combined well. Pour into the flour mixture and mix on low to thoroughly combine. Do not overmix or the doughnuts will be tough. Allow to rest, 10 minutes.
Transfer the dough to a doughnut dropper or a pastry bag fitted with a 1/3-inch round tip; a small ice cream scoop can also be used to make doughnut holes. Drop several doughnuts into the oil and cook until light golden brown, 1 to 2 minutes per side. Transfer to a rack to cool. Repeat with the remaining dough.
Beat together the cream and confectioners' sugar with a mixer on high speed until medium-stiff peaks are formed.