Cut an X about 1/2 inch long through the flat side of each chestnut shell. Place nuts in a 12- by 17-inch pan.
Bake in a 400° oven until shells begin to split open and nuts are slightly soft (break 1 open to test), 25 to 30 minutes. Hold 1 hot nut at a time in a soft potholder and squeeze to loosen shell. Pull off shell and brown skin; use a small, sharp knife to pull bits of skin from crevices. Discard any moldy or hard, dried nuts.
Meanwhile, in a 5- to 6-quart pan over medium-high heat, frequently stir onion, celery, and fennel seed in 1 tablespoon oil until vegetables are limp, 8 to 10 minutes.
Add broth and chestnuts; bring to a boil over high heat. Reduce heat, cover, and simmer until chestnuts mash easily, about 40 minutes.
Whirl mixture, a portion at a time, in a blender or food processor until smooth.
Return purée to pan and add half-and-half. Stir over medium-high heat until steaming, about 3 minutes (about 8 minutes if chilled).
Meanwhile, in a 10- to 12-inch frying pan over medium heat, frequently stir currants and pine nuts in remaining 1/2 tablespoon oil until nuts are golden, 3 to 5 minutes. Pour into a small bowl.
Ladle soup into bowls and top equally with currant-pine nut mixture. Season to taste with salt and pepper.