Melt the butter in a medium skillet over medium heat. Add the celery and green onions and stir for 5 minutes, or until the onions are translucent. Transfer the vegetables to a large bowl and set it aside.
Slice the hot dogs lengthwise into quarters, then slice them into thirds. In the same skillet, cook the hot dogs until they're lightly browned, about 5 minutes. Add them to the bowl of celery and onions and stir. Set aside 1 cup of the hot dog mixture.
Preheat the oven to 400 degrees Fahrenheit.
In another large bowl, whisk together the eggs, milk, sage, and pepper. Add the hot dog mixture, except for the reserved 1 cup. Stir in cornbread and 1 ½ cups of shredded cheese until it's well combined.
Pour the cornbread mixture into a shallow 3-quart baking dish. Top it with the reserved hot dog mixture and the remaining ½ cup of shredded cheese.
Bake it for 30 minutes or until golden brown. Serve it and enjoy!