To make the caramelized onions, heat pan over low-medium heat. Add olive oil to skillet. Separate onion slices into rings and add to your skillet. Sprinkle with salt. Stir occasionally and watch to make sure they are cooking up nice and slow; caramelizing onions takes a bit of time, so don’t rush the process by turning up the heat. Continue cooking for about 45 minutes or until onions are deep, golden brown and they have a marmalade consistency. Remove from heat and serve. Extra onions can be refrigerated for up to a week, or frozen up to 6 months.
To make the Russian dressing, mix all ingredients together. Taste and adjust seasonings. Store extra in the refrigerator for up to a week. Use on sandwiches, veggie burgers, or salads.
Heat and lightly oil grill. Cook hot dogs according to package directions. Open buns and toast on the grill. Place half a slice of vegan cheese in the bun. Put hot dog on top, then a tablespoon or two of each of the following; caramelized onions, Russian dressing, and sauerkraut. Serve immediately.