Thoroughly grease a 12 cup Bundt pan. In a medium bowl combine the flour, baking soda, baking powder, cinnamon, and salt. In a large mixing bowl combine the sweet potatoes, oil, and sugar. Beat until smooth. Add eggs two at a time, beating well between each addition. Add the flour mixture and beat until just blended. Add the vanilla and mix to incorporate. Transfer the batter to the Bundt pan.
Bake for 1 hour and 5 minutes or until a cake tester comes out mostly clean. Cool the cake in the pan for about 15 minutes, then invert onto a cake platter.
For the icing, sift the powdered sugar into a medium bowl. In a small saucepan, stir the brown sugar, cream, and butter on med-low heat until the sugar dissolves. Increase the heat to a boil. Boil for 3 minutes, stirring occasionally. Remove from the heat and stir in the vanilla. Pour the mixture over the powdered sugar and whisk until it is smooth and lightened in color. Cool the icing until it is lukewarm and falls in thick ribbons from the whisk. Spoon over the cake allowing the icing to flow slowly down the sides.