In a large pot over medium heat, melt the butter. Add onion, carrot, and celery; cook until vegetables soften and edges look glossy, about 5 minutes.
2 tablespoons unsalted butter, 1 cup onion, 0.5 cup carrot, 0.5 cup celery
Stir in garlic and cook until fragrant, about 30 seconds.
2 cloves garlic
Thickener
Sprinkle in flour and stir constantly for 1 minute to cook out the raw taste.
Soup
Gradually whisk in chicken broth, scraping any bits from the pot. Bring to a gentle boil, then stir in corned beef and sauerkraut. Reduce heat and simmer until flavors meld, about 10 minutes.
0.33 cup all-purpose flour, 4 cups chicken broth
Finishing
Remove from heat and stir in Swiss cheese until it melts into a silky ribbon.
2 cups corned beef
Return to low heat, stir in heavy cream and Thousand Island dressing, and season with salt and pepper to taste.
1 cup sauerkraut, 1 cup Swiss cheese
Notes
During prep, I found that cutting onion, carrot, and celery into uniform dice ensures even cooking.When melting Swiss cheese, adding it off the heat helps maintain a silky texture.From storage tests, frozen soup reheats evenly without separating when stirred halfway through.