1) Preheat the oven to 350°F. Lightly grease a pumpkin mini cheesecake pan, or a 9" x 9" or 7" x 11" pan.
2) Beat together the oil, eggs, sugar, pumpkin, spices, salt, and baking powder till smooth.
3) Add the flour, stirring just until smooth.
4) Fill the wells of the pumpkin mini cheesecake pan about 3/4 full; use a scant 1/4 cup of batter in each well.
5) If you're using a 9" square pan or 7" x 11" pan, pour the batter into the pan.
6) Bake the mini cakes for 20 minutes, or until a cake tester inserted into the center of one comes out clean. Bake the sheet cake for about 30 minutes, till it tests done the same way.
7) Remove the cake(s) from the oven, and allow to cool. Remove the mini cakes from the pan after about 5 minutes, transferring them to a rack to cool. The sheet cake can cool right in the pan.
8) While the cakes are cooling, prepare the icing. If the butter and cream cheese are cold, warm them very briefly in the microwave, just till they feel soft but haven't begun to melt.
9) Beat together the cream cheese, butter, sugar, and vanilla till smooth.
10) Spread the soft frosting atop the cooled cake(s).
11) Sprinkle with the crystallized ginger.