In a small bowl, cover currants with very hot water. Let sit for 10 minutes; drain.
Meanwhile, combine flour, semolina, and salt. In the bowl of a stand mixer, beat butter and sugar until smooth. Add egg, scrape down inside of bowl, and mix until combined. Add flour mixture, orange zest, and currants, mixing slowly until combined. Turn dough onto a work surface and shape into a disk. Wrap in plastic wrap and chill at least 2 hours and up to 2 days.
Preheat oven to 350°. Unwrap dough, place on a floured work surface, and roll 1/3 in. thick. Evenly sprinkle 2 baking sheets with about 1 tbsp. cornmeal each. Cut dough with a 2-in. decorative cutter and place slightly apart on baking sheets, rerolling scraps as needed.
Bake cookies until light golden brown, 10 to 12 minutes, switching pan positions halfway through cooking. Transfer cookies to a rack to cool.
*Find in the baking aisle of well-stocked markets.