Preheat the oven to 375 degrees F and line a 9-by-13-inch baking sheet with parchment.
Slice off and discard the ends of each hot dog. Quarter the trimmed hot dogs, crosswise. Unroll the crescent roll dough on the prepared baking sheet. Split the dough in half lengthwise. Pinch the perforated seams of the dough together.
For the chili dog bites: Evenly space 6 teaspoon-size dollops of chili down the center of one strip of dough. Top each with some onions and Cheddar. Stand a hot dog piece upright in each pile of toppings. Fold the sides of the dough on the chili dog bite lengthwise to cover the filling, leaving holes for the hot dogs to stick out. Pinch the dough together between each hot dog. The filling should be sealed inside and the hot dogs peeking out. Use the dull side of a butter knife to score the dough between each hot dog. Brush the dough with egg and sprinkle with the sesame seeds.
For the Chicago dog bites: Arrange the remaining 6 hot dog pieces standing upright on the other dough strip. Nestle against each hot dog half a cornichon, half a tomato and a teaspoon relish. Fold and seal as the chili dog bites above. Brush the dough with the egg and sprinkle with poppy seeds.
Bake until golden brown, 15 to 17 minutes. Cool for 5 minutes. Pull-apart and serve with yellow and spicy brown mustard for dipping.
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