Combine butter, white sugar, brown sugar, corn syrup and 1/4 cup half and half in a large microwavable bowl (I used a 4 cup glass bowl). Cook 6 minutes stirring every 90 seconds. Let cool about 3-4 minutes and add in the remaining 2 tablespoons half & half (be careful it doesn't bubble up). Stir until smooth and pour into a small greased dish to cool completely.
Combine flour, ginger, cinnamon, baking soda & salt in a small bowl. Mix with a whisk and set aside.
With mixer on medium, cream shortening, butter and sugar until fluffy. Add in molasses and egg.
With mixer on low, add in flour mixture until completely combined.
Preheat oven to 350 degrees.
Combine 1/3 cup each white and brown sugar in a small bowl. Set aside.
Pull off about 1/2 tablespoon of caramel from your cooled caramel and form into a small ball. Wrap 2 tablespoons of cookie dough around the caramel and roll into a ball. Roll the ball in the sugar mixture.
Place about 1 1/2" apart on a parchment lined pan and bake 9 minutes or until edges are slightly browned.
Cool 5 minutes on the pan before moving to a wire rack to cool completely.