Step 1In the bowl of a stand mixer or in a large bowl using an electric mixer, beat the butter and sugar until light and fluffy, 3 to 5 minutes. Add the milk, vanilla and egg, and beat over low speed just to incorporate.
Step 2In a separate mixing bowl, whisk together the flour, lime zest, baking powder, pepper and salt, breaking up any lumps.
Step 3With the mixer on low speed, slowly incorporate the dry ingredients into the butter mixture.
Step 4Place dough on a sheet of plastic wrap and roll into a log shape about 2 inches in diameter. Wrap in plastic wrap and refrigerate until chilled, about 1 hour.
Step 5Heat the oven to 350 degrees. Remove the dough log and slice crosswise into cookies one-fourth inch thick. Place the cookies on a lightly greased baking sheet and bake until a light golden brown, 10 to 15 minutes.
Step 6Remove the cookies and cool on a rack. Dust the cooled cookies lightly with confectioner's sugar (and black pepper, if using).