Heat oven to 375°F. Spray 9-inch square or 11×7-inch (2-quart) glass baking dish with cooking spray. Pour hot chili into dish; spread evenly.
Unroll dough; cut into 4 strips. Cut 1 cheese stick in half lengthwise; place 1 half on each side of 1 hot dog. Wrap pizza dough strip around cheese and hot dog, overlapping slightly in center. Repeat with remaining dough strips, cheese sticks, and hot dogs. Place wrapped hot dogs on top of hot chili. (Chili must be hot.)
Bake 15 to 20 minutes or until dough is light golden brown.
Meanwhile, in a small microwavable cup, microwave butter on High until melted. Stir in garlic powder and parsley.
Remove baking dish from the oven. Brush on top of each cheese dog with butter mixture. Serve immediately.