In a small bowl, combine all the ingredients for the Russian dressing and set aside.
In a skillet over medium heat, add oil. Once hot, add the meat and cook just until heated through.
Lightly butter one side of each slice of bread and place them butter-side down on a plate.
On one slice of bread, spread a layer of Russian dressing, then layer the meat, cheese, and sauerkraut. Place the other slice of bread on top. Repeat until all sandwiches are assembled.
In the same skillet, cook the sandwiches over medium heat for 4-6 minutes per side, until the cheese melts and the bread is golden and crispy.