Preheat your oven to 350°F (175°C) and prepare a 9x13 inch baking pan by greasing it with butter or cooking spray and dusting it with flour.
In a medium bowl, whisk together the all-purpose flour, baking soda, ground ginger, ground cinnamon, ground cloves, and salt.
In a large mixing bowl, cream together the softened unsalted butter and packed brown sugar until light and fluffy, about 2-3 minutes. Then beat in the molasses and large eggs until well combined.
Gradually add the dry mixture to the wet ingredients, alternating with the buttermilk, starting and ending with the dry ingredients. Mix gently until just combined.
Pour the batter into the prepared baking pan and bake for 30-35 minutes. Check for doneness with a toothpick.
Allow the cake to cool in the pan for about 10 minutes before transferring it to a wire rack to cool completely.
In a mixing bowl, beat the softened unsalted butter until creamy. Gradually add the powdered sugar, molasses, and ground cinnamon, mixing until smooth and fluffy. Adjust consistency with milk as needed.
Once the cake is completely cool, frost it with the cinnamon frosting using a spatula.