Preheat oven to 350 degrees, with rack in center. Line a baking sheet with parchment paper; set aside. In a medium bowl, whisk together flour, cornmeal, baking powder, and salt; set aside.
In the bowl of an electric mixer fitted with the paddle attachment, cream butter and sugar on medium speed until light and fluffy, about 2 minutes. Beat in eggs one at a time until well combined; beat in orange extract and zest. Add flour mixture; beat on low speed until just combined. Beat in dates, almonds, and anise.
Transfer to prepared baking sheet; using your hands, pat into a slightly flattened log, about 15 by 4 inches. Bake until firm and lightly browned, and top is slightly cracked, 30 to 35 minutes. Let cool on a wire rack 15 minutes.
Transfer to a cutting board. Using a serrated knife, cut log crosswise into 1/2-inch-thick slices. Arrange on a wire rack on a rimmed baking sheet. Bake, rotating sheet halfway through, until slices are just turning brown around the edges, 15 to 18 minutes. Transfer to a wire rack to cool.