Remove the core from the cabbage and slice it as thinly as possible (a mandoline works well for this).
Melt the butter in a large skillet over medium heat. Add the cabbage, season with salt and sauté until soft, 5 to 6 minutes. Add the vinegar and sugar and continue cooking, stirring frequently, until all the liquid has evaporated, 3 to 4 minutes longer. Transfer to a bowl and set aside.
In a separate bowl, combine the mayonnaise, chili sauce and dill relish. Cover and refrigerate until ready to use.
Preheat a gas or charcoal grill to medium heat. Score the hot dogs at 1-inch intervals on 2 opposite sides. Oil the grill grates, add the hot dogs and cook for 7 to 10 minutes, turning them frequently with tongs as they cook.
Place the hot dogs in toasted buns, top with the mock sauerkraut and Thousand Island spread and serve along with our Speedy Stovetop "Baked" Beans.
Notes
Recipe Notes:
There are a lot of high-quality brands of hot dogs to choose from today. For best results, look for an uncured variety that's been minimally processed and has all-natural ingredients.