Preheat oven to 375ºF. Pour 1 pouch of chili into a colander and set inside sink to drain. While chili is draining, line a baking sheet with parchment paper. Lay long end of crescent rolls out in a ring, overlapping them to form a base.
Slice each hot dog into rings, without cutting all the way through to the bottom, to make them bendable. Lay hot dogs on base of crescent ring. Spoon drained chili over hot dogs. Sprinkle carefully with grated cheese.
Fold ends of crescent dough up and over the filling. Tuck ends underneath ring. Bake for 15 minutes or until golden brown. While ring is baking, heat second package of chili according to package directions
Pour chili into center of baked ring and sprinkle with more cheese, as desired. Serve immediately.