Heat your oven to 350°F (175°C) before you start mixing the batter. Coat a 9×13-inch baking pan with butter or baking spray, then dust it lightly with flour. You can also line the pan with parchment paper if you want the cake to lift out easily after baking.

Place the shortening or softened butter and granulated sugar into a large mixing bowl. Beat until the mixture looks light and fluffy. Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract and applesauce until everything is smooth and well blended.

In a separate bowl, combine the flour, baking soda, cinnamon, nutmeg, cloves, ginger, allspice, and salt. Give everything a good whisk so the spices are evenly mixed throughout the flour.

Slowly add the dry ingredients to the wet mixture, stirring just until everything comes together. Fold the drained raisins into the batter using a spatula. Stop mixing once the flour disappears to keep the cake soft and tender.

Pour the batter into the prepared pan and smooth the top. Place it in the oven and bake for 30 to 35 minutes. Check for doneness by inserting a toothpick into the center. If it comes out clean, remove the cake from the oven and let it cool completely on a wire rack.

Beat the softened cream cheese and butter until silky and creamy. Add the powdered sugar a little at a time, then mix in the vanilla extract and lemon juice. If the frosting feels too thick, stir in a small splash of milk until it spreads easily.

Once the cake has cooled completely, spread the frosting evenly over the top. Cut into 12 equal pieces and serve. For an even richer flavor, refrigerate the frosted cake for about an hour before slicing. The spices become more pronounced, and the frosting firms up beautifully.