To make the cupcakes:
Preheat the oven to 350ºF. Line a twelve-well cupcake tin with cupcake liners or spray with nonstick cooking spray.
In a medium bowl, whisk together the flour, baking powder, salt, cinnamon, cloves, allspice, nutmeg, and pepper.
Using a stand mixer fitted with the paddle attachment, mix the eggs, granulated sugar, brown sugar, molasses, vegetable oil, and ginger on medium speed until well combined, scraping down the sides of the mixer with a spatula. Add the flour mixture and milk in three intervals, starting and ending with the flour. Mix until smooth.
Using an ice cream scoop, fill each well three-quarters full of batter. Bake until a toothpick inserted in the center comes out clean, 20 to 25 minutes. Remove the cupcakes from the oven and let sit for 5 minutes. Transfer them to a wire rack to cool completely.
To make the buttercream:
Using a stand mixer with a whisk attachment, mix the butter and molasses on medium speed until light and fluffy, about 3 minutes. Add the confectioners’ sugar and mix on low speed until well incorporated, scraping down the sides of the mixer with a spatula. Add the cream and salt and beat on medium speed until smooth, about 3 minutes.
Transfer the buttercream to a piping bag or a resealable plastic bag with the end snipped off. Pipe the frosting onto the cupcakes. Alternately, spread the frosting with a small offset spatula.