Preheat your oven to 350°F (175°C). Line a standard 12-cup muffin tin with paper liners to ensure the cupcakes don’t stick and are easy to remove after baking.
In a medium bowl, whisk together the flour, ground ginger, cinnamon, cloves, nutmeg, baking powder, baking soda, and salt. Setting these aside ensures the leavening agents and spices are evenly distributed.
In a large mixing bowl or using a stand mixer, beat the softened butter and brown sugar together until the mixture is light and fluffy. This should take about 2 to 3 minutes on medium speed.
Add the egg and beat well. Mix in the molasses and vanilla extract until fully combined. Don’t worry if the mixture looks slightly curdled at this stage; it will come together once the flour is added.
Turn the mixer to low speed. Add the dry ingredients in three parts, alternating with the milk in two parts. Begin and end with the dry ingredients. Mix only until just combined to keep the cupcakes tender.
Divide the batter evenly among the cupcake liners, filling each about two-thirds full. Bake for 18 to 22 minutes, or until a toothpick inserted into the center comes out clean. Transfer to a wire rack to cool completely.
Beat the softened butter until smooth. Gradually add the powdered sugar, one cup at a time. Mix in the molasses, cinnamon, and heavy cream. Beat on high for 2 minutes until the frosting is light and airy.
Once the cupcakes are entirely cool, pipe or spread the molasses buttercream onto each cupcake. You can use a star tip for a festive look or a flat spatula for a rustic finish.