Combine the carrots, okra, salt, jalapenos, garlic, celery and red bell peppers in a bowl. Add just enough water to submerge the vegetables. Cover and refrigerate overnight.
Drain and rinse the vegetables. In a clean bowl, mix the oil, vinegar, oregano and pepper. Add the vegetables and mix well. Marinate the mixture overnight in the refrigerator.
Preheat the grill to medium-low heat. Grill the hot dogs until charred, about 10 minutes.
Serve the hot dogs in the buns. Spoon some okra mixture over the hot dogs. Place leftover giardiniera in Mason jars and store in the refrigerator for 2 to 3 weeks.