Preheat oven to 350°F. In large bowl, beat butter, powdered sugar, orange juice and vanilla just until mixed through. Stir in flour. If dough is too crumbly mix in 1-2 tablespoons half and half.
On a lightly floured surface roll dough out to 1/2 inch thick. Cut into small shapes by hand or use cookie cutters. You can also use a glass for round cookies. Smear with a bit of softened butter or shortening to prevent sticking.
Place cookies 1/2 inch apart on ungreased cookie sheet.
Bake 12 to 16 minutes (depends on size) or until set. Bottoms should be light golden brown. Immediately remove from cookie sheet to wire rack. Cool completely, about 30 minutes.
For Chocolate Dipping:
In small microwavable bowl, microwave chocolate chips and shortening uncovered on high power for 1 minute. Stir. If it's not smooth, microwave for 15 seconds increments until melted. Stir until smooth. Dip half of each cooled cookie into melted chocolate. Place on waxed paper until chocolate is set.