Preheat the oven to 350 degrees F (175 degrees C). Combine shortening, vegetable oil, and flour in a bowl; mix very well. Brush two 9x9-inch cake pans with the mixture. Reserve remaining mixture for future baking.

Beat sugar, eggs, oil, and vanilla extract together in a large bowl.

Mix flour, baking powder, baking soda, cinnamon, pumpkin pie spice, and salt together in a separate bowl. Add to the sugar mixture gradually, mixing constantly to prevent lumps. Stir in sweet potatoes. Fold in chopped pecans. Divide batter between the prepared pans.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, 40 to 45 minutes. Let cool in the pans for 15 minutes, then turn out onto a wire rack and cool completely, about 1 hour.

Make the frosting while cakes are cooling. Combine confectioners' sugar, cream cheese, butter, vanilla extract, orange zest, and allspice in a medium bowl. Beat until smooth and creamy.

Place 1 cooled cake layer on a serving plate. Cover with frosting. Add second cake layer. Frost the top and sides. Sprinkle pecans on top.