1. Break off and discard the tough, thick end of each asparagus spear.
2. Chop the spears into 1/4-inch slices and add to the crock pot along with all remaining ingredients down to and including the white pepper.
3. Add water to within 1 inch of the top of the crock pot.
4. Cover the crock pot and cook on high for 6-7 hours.
5. About two hours before serving, use a slotted spoon to remove most of the vegetables to a blender.
6. Use a ladle to add some of the liquid from the crock pot to the blender.
7. Puree the mixture and add back in to the crock pot.
8. Repeat once or twice more as necessary (you can leave some of the pieces in the crock pot for effect.) Add approximately 1 cup of the half-and-half to the crock pot.
9. Add the corn starch to the remaining half-and-half in the carton.
10. Close the carton well and shake vigorously.
11. Add the mixture to the crock pot.
12. Continue to cook on high for 1 hour, stirring occasionally.
13. Serve in bowls with a dollop of sour cream and chopped chives sprinkled on the sour cream.