Preheat oven to 325 degrees. Grease an 8-by-8-inch baking pan and set aside. In a medium bowl, combine flour and soda.
In a large bowl, blend sugar and butter to form a grainy paste. Add syrup, egg and vanilla. Beat at medium speed until smooth. Add flour mixture and pecans. Blend at low speed just until combined.
Pour batter into baking pan and smooth top with spatula. Bake 40 minutes, or until a toothpick inserted in the center comes out clean. Cool in pan for 15 minutes, then invert onto cooling rack; cool completely before frosting.
Meanwhile, in a medium bowl, cream butter and cream cheese. Add brown sugar and sorghum, beating until smooth. Reduce mixer speed and slowly add confectioners’ sugar, mixing until smooth.
Spread frosting on cooled bars, cut and garnish each with a toasted pecan half.