Melt 2 tablespoons butter in a large stockpot over medium heat.
Add in celery, onion, garlic, salt, and pepper.
Cook, stirring often, until the celery is tender, about 5-10 minutes.
Reduce heat to low.
In a small bowl, whisk together 2 tablespoons melted butter, flour, and 1/4 cup chicken broth.
Slowly whisk mixture into the stockpot and cook, stirring constantly, for 2 minutes.
Slowly whisk in the remaining 2 3/4 cups chicken broth, then pour in half and half, Russian dressing, potatoes, sauerkraut, and corned beef.
Increase heat back to medium, bring to a simmer, stirring occasionally.
Cover and simmer (you'll probably need to lower the heat back to low) until the potatoes are cooked, about 15 minutes, stirring occasionally.
Remove from heat, stir in shredded swiss cheese until melted.
Taste and re-season, if necessary, and serve with toasted marbled rye bread!