Preheat the oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking pan.

Whisk together flour, cinnamon, baking powder, baking soda, salt, cloves, nutmeg, and allspice in a bowl until well combined.

Cream together butter, brown sugar, and white sugar in a large bowl with an electric mixer until light and fluffy. Beat in eggs, 1 at a time, mixing well after each addition. Mix in vanilla extract. Add in half of the flour mixture, and stir until just combined. Pour in buttermilk, and mix until just combined. Add in remaining flour mixture and mix until just combined. Pour batter into the prepared pan and spread into an even layer.

Bake in the preheated oven until the middle of the cake springs back lightly when touched, 40 to 45 minutes. Remove from the oven and allow the cake to cool completely before frosting.

For the frosting, cream butter in a large bowl until smooth. Add cream cheese and beat until thoroughly combined. Mix in confectioners' sugar, 1 cup at a time, and beat until smooth after each addition. Mix in vanilla and salt. Add in heavy cream and beat until frosting is smooth, about 2 minutes. Frost cooled cake as desired.