Beat butter, sugar, and sorghum together in a bowl until creamy. Mix all-purpose flour, anise, baking soda, cinnamon, and salt together in a separate bowl; stir into butter-sugar mixture until just incorporated. Roll dough into 1-inch thick logs. Arrange logs on a baking sheet and refrigerate 8 hours or overnight.
Preheat oven to 350 degrees F (175 degrees C).
Slice dough into small cookies; arrange on baking sheets.
Bake cookies in the preheated oven until lightly browned, 8 to 9 minutes.