Preheat oven to 350°F (175°C). Grease and flour a 9-inch round cake pan.
In a bowl, whisk together flour, baking soda, cinnamon, ginger, nutmeg, cloves, and salt.
In another bowl, beat butter, granulated sugar, and brown sugar until light and fluffy.
Add molasses and egg; mix until smooth.
Alternate adding flour mixture and buttermilk, starting and ending with flour. Mix just until combined.
Pour batter into the prepared pan and smooth the top.
Bake 35–40 minutes, or until a toothpick comes out clean.
Cool completely in pan on a wire rack.
For the frosting, beat cream cheese and butter until smooth. Add molasses, cinnamon, and vanilla.
Gradually beat in powdered sugar until fluffy.
Frost the cooled cake and serve.