Heat oven to 350 degrees. Oil a 9-by-13-inch metal baking pan and line it with a piece of parchment paper that hangs over the two long sides.
In a large bowl, whisk to thoroughly combine the oil, brown sugar, eggs, buttermilk, cinnamon, ginger, nutmeg, allspice, cloves and salt.
Add the flour, baking powder and baking soda and whisk until smooth. A few small lumps are OK.
Scrape the batter into the prepared pan and spread it in an even layer. Bake until the cake is golden brown and a skewer inserted into the center comes out clean, 30 to 35 minutes. Let the cake cool in the pan for 15 minutes before using the parchment paper to lift it out and set on a cooling rack to cool completely.
While the cake cools, make the frosting.
Top the completely cooled cake with swoops and swirls of frosting and serve immediately, or cover and store at room temperature for 2 days (or a little longer in the fridge).
