Preheat oven to 350 degrees F with rack in middle. Grease an 8- or 9-inch square cake pan or 8-inch round cake pan with butter or nonstick spray and line the bottom with parchment paper.
In a small bowl, place the raisins and bourbon. Cover and heat in the microwave for 30 seconds (or you can heat on a small saucepan on the stove). Set aside to cool for at least 15 minutes.
In a medium mixing bowl, whisk together the all-purpose flour, whole wheat flour, baking powder, baking soda, and salt, cinnamon, nutmeg, and cloves.
In a large mixing bowl or the bowl of a stand mixer fitted with the paddle attachment, beat the butter, brown sugar, honey, and vanilla on high speed until the mixture is pale and fluffy, about 2 to 3 minutes, stopping to scrape down the bowl once or twice as needed.
Add the eggs, one at a time, beating after each addition until fully incorporated. The batter will look curdled, which is absolutely fine.
Beat in the applesauce, stopping as soon as it is combined.
Reduce the mixer speed to low and gradually add the flour, stopping as soon as it disappears.
By hand with a rubber spatula, fold in the raisins with their liquid and the pecans.
Scrape into the prepared pan and smooth the top. Bake for 32 to 38 minutes, until golden brown on top and a toothpick inserted in the center comes out clean. Place the pan on a wire rack and let cool in the pan for 15 minutes.
With a dull knife, loosen the edges of the cake from the pan, then unmold it and place it on the rack, dome-side up, to finish cooling completely. (I like to invert from the pan onto a plate, then re-invert it back onto the cooling rack). Let cool completely.
Make the frosting: In the bowl of a standing mixer fitted with the paddle attachment, place the cream cheese, butter, bourbon, vanilla, cinnamon, and salt. Beat on medium speed until smooth. Reduce the mixer speed to low, then slowly add the powdered sugar. Once the sugar has been incorporated, stop and scrape down the sides, then beat a bit more, until combined and creamy. Spread over the top of the cooled cake (I leave the sides bare). Enjoy!
TO STORE: Refrigerate the applesauce cake for up to 5 days. Let it sit at room temperature for 15 minutes or so prior to serving.
TO FREEZE: Freeze cake in an airtight, freezer-safe storage container for up to 3 months. Let thaw overnight in the refrigerator, then let sit at room temperature for 15 minutes or so before serving.