In a bowl, mix soy sauce, apple cider vinegar, olive oil, smoked paprika, minced garlic, and black pepper.
Place the tempeh slices in the marinade and let them soak for at least 30 minutes.
Heat a skillet over medium heat, add some oil, and sauté the tempeh slices for 3-4 minutes per side until golden and crispy.
In a bowl, combine vegan mayo, ketchup, relish, apple cider vinegar, salt, and pepper, then whisk until smooth.
In a pan, heat sauerkraut over low heat for 2-3 minutes.
Toast the rye bread lightly.
Spread Russian dressing on both slices of bread.
Arrange the sautéed tempeh, heated sauerkraut, and vegan cheese in layers.
Butter the outside of the bread slices. Grill on a skillet over medium heat for 3-4 minutes on each side until the bread is golden brown and the cheese melts.
Slice in half and serve hot with pickles or chips.