Melt the butter in a large pot over medium heat. Add the chopped onion and minced garlic, stirring frequently until the onion becomes translucent and fragrant, about 5 minutes.

Sprinkle the flour over the onion mixture and stir constantly to create a roux. Cook for 2 minutes, stirring continuously to prevent burning. The mixture should turn a light golden color.

Gradually pour in the chicken broth while whisking constantly to prevent lumps. Bring the mixture to a gentle simmer (about 3-5 minutes), then reduce the heat to low.

Stir in the heavy cream and mix until fully incorporated. Add the chopped corned beef and well-drained sauerkraut, stirring well to distribute everything evenly.

Add the shredded Swiss cheese and Russian dressing. Keep heat on low and stir gently until the cheese melts completely. Low heat prevents the cheese from becoming stringy. Taste before adding salt since corned beef and sauerkraut are already salty. Add pepper and adjust salt only if needed.

Let the soup simmer gently for 10 minutes, stirring occasionally. Serve hot, garnished with rye bread croutons and fresh chopped parsley.