Whisk the flour, polenta, 1 teaspoon pepper, the baking powder and salt in a small bowl.
Beat the butter and granulated sugar in a large bowl with a mixer on medium speed until light and fluffy, about 1 minute. Beat in the cheese, then the egg. Mix in the flour mixture until the dough just comes together.
Divide the dough between 2 sheets of plastic wrap. Shape each piece into a log and wrap in the plastic. Press the sides of the logs against the counter to form compact square-sided logs, about 7 inches long and 1 inch wide. Freeze the logs until firm, about 45 minutes.
Preheat the oven to 350 degrees F. Line 2 baking sheets with parchment paper. Stir the sanding sugar and remaining 1/2 teaspoon pepper in a small bowl. Trim the ends of the logs. Cut into 1/4-inch-thick slices and arrange 1 inch apart on the prepared pans. Sprinkle with the sugar-pepper mixture.
Bake, switching the pans halfway through, until the cookies are crisp and golden on the bottom, 12 to 16 minutes. Let cool completely on the pans.