First, create the cheese portion of this dip. To a large saucepan, melt the butter. Add the yellow onion and cook until tender, about 4 minutes. Whisk in the flour and cook for an additional 2 minutes. Whisk in the milk and bring to a simmer. Lower the heat to low and cook until thickened, about 2 minutes. Stir in the cheese, tomatoes with chilies, tabasco, and salt and black pepper to taste. Cover and keep warm.
Next, create the chili portion of this dip. Melt the butter in a large nonstick skillet over medium heat. Add the onion and cook until tender, about 4 minutes. Add the ground beef and cook until brown and cooked through, about 7 minutes. Stir in the chili seasoning, tomato sauce, ketchup, yellow mustard, Worcestershire sauce, brown sugar, chili powder, and salt and black pepper to taste. Stir to combine and cook over medium-low heat for about 20 minutes to allow the flavors to meld. Stir in the hot dog pieces and continue cooking for 2-3 minutes or until heated through. Remove from heat and transfer to a large serving bowl.
Swirl the cheese sauce into the chili, creating a swirl-like design. Alternatively, you may fold the cheese sauce completely into the chili. Garnish with fresh green onions and serve with tortilla chips, celery, and carrots. Enjoy!