For the bread: Adjust an oven rack to the middle position and preheat the oven to 350F [180C]. Grease and line a 9 x 4 x 4-inch Pullman Pan (affiliate link) with parchment paper (a 9 x 5 inch pan will also work). In a medium bowl, whisk together the flour, cinnamon, ginger, nutmeg, cloves, baking powder, baking soda, and salt.
In the bowl of a stand mixer fitted with the whisk attachment, combine the pumpkin puree, oil, vanilla, and granulated sugar. Whisk on medium-low until just combined, about 1 minute, using a rubber spatula to scrape down the bottom and sides of the bowl as necessary. Add the eggs one at a time, adding the next egg only after the previous one has been fully incorporated, scraping down the bottom and sides of the bowl after each addition. With the mixer on low, gradually add the dry ingredients and whisk until just combined. Scrape down the bottom and sides of the bowl once more, and whisk on medium for an additional 15 seconds.
Pour the batter into the prepared pan and use an offset spatula to smooth the top. Set the bread pan on a sheet pan and bake for 50 to 65 minutes, or until a skewer inserted into the center of the cake comes out with a few crumbs attached. Move the pan to a wire rack and let cool for 20 minutes, then use the parchment sling to remove the bread from the pan. Let cool to room temperature before covering the top with the cream cheese icing. The cake can be stored at room temperature, in an airtight container, for 3 days without icing, and refrigerated for 2 days with icing.
For the icing: In the bowl of a stand mixer fitted with a paddle, beat the butter, cream cheese, and salt on medium until smooth and creamy. Add the confectioners’ sugar and mix on low until combined. Scrape down the sides of the bowl and mix on medium until the icing is light and fluffy, 3 to 4 minutes (If the frosting is too loose for your liking, add 1 tablespoon confectioners’ sugar at a time, beating on low after each addition, until the desired consistency is reached). Add the vanilla and mix on low until combined.