In the bottom of a large bowl, combine mustard, vinegar, sugar, and about 3 tablespoons of vegetable oil. Add the onions, cabbage, romaine, tomatoes, and pickles and toss the salad. Season with salt and pepper, adjust seasonings, and reserve.
Heat a large nonstick skillet over medium-high heat. Add in remaining 1 tablespoon vegetable oil (1 turn of the pan) then arrange the sliced dogs in a single layer. Sear them a couple of minutes on each side. Remove to paper towels to drain.
Mound up the salad on plates, top with seared dogs, and serve.