For the NY Onion Sauce: Heat oil in a medium saucepan over medium heat. Add onions and cook until soft. Stir in the cinnamon and chili powder and cook for 1 minute. Add the ketchup, water, hot sauce and salt and black pepper and bring to a simmer. Cook mixture for 10 to15 minutes or until thickened. Transfer to a bowl and let cool to room temperature before serving.
For the Roasted Red Pepper Relish: Combine all ingredients in a medium bowl and let sit at room temperature for 30 minutes before serving.
For the hot dogs: Heat the grill to high. Grill dogs until golden brown on all sides, about 7 minutes. Remove to a plate. Place buns on the grill cut side down and grill until lightly golden brown, about 20 seconds.
For assembly: Place hot dog into prepared bun. Top with NY Onion Sauce, Horseradish Mustard and then with the Roasted Red Pepper Relish.