In a medium bowl, stir together the flour, baking powder, spices, and salt. In a larger bowl, beat the butter, oil and sugar until light and fluffy. Beat in the eggs and vanilla.
Add about 1/3 of the flour mixture to the butter mixture and stir it in by hand or with the electric mixer on low speed, just until it’s combined. Add about half the milk in the same manner, then another third of the flour, the rest of the milk, and the rest of the flour, mixing just until the batter is blended.
Fill a prepared 9" x 13" baking dish that has been lined with parchment paper. Bake for 25 minutes, or until an inserted toothpick comes out clean. Let cool completely before cutting out and frosting. Makes about 8 2" diameter cakes.
To make the frosting:
In a small bowl or pot, stir together the brown sugar, water and vanilla. Stir it occasionally until the sugar is more or less dissolved.
In a medium bowl, beat the butter until creamy; add in the confectioner's sugar and about 3/4 of the brown sugar syrup and beat until smooth. Add more sugar or syrup as needed until you have a soft, spreadable icing.