Preheat oven to 350 degrees F. Butter and line the bottom of a 13″ x 9″ baking pan with parchment paper. Butter paper.
In a medium bowl, combine flour, baking powder, fresh and ground gingers, black pepper, and salt.
In a large bowl of an electric mixer fitted with the paddle attachment, or with a hand mixer, beat butter and granulated sugar on medium speed until light and fluffy, about 2 minutes.
Turn the mixer to low speed, add honey and molasses, and beat until incorporated, about 2 more minutes. Beat in eggs.
Adjust the mixer to a low speed, beat flour into sugar mixture in three additions, alternating with milk, until well combined
Pour batter into prepared baking pan. Bake in center of the oven at 350 degrees F. for 33 to 35 minutes, or until a toothpick inserted in the center of the cake comes out clean.
Remove cake from oven and let cool for 5 minutes. Invert the cake onto a wire rack. Remove parchment and flip the cake over, onto a rack over a cookie sheet. The cake should be top side up, and over a sheet or piece of parchment to collect any running glaze.