Heat a large stockpot over medium heat. Cook and stir onion, celery, red bell pepper, butter, garlic, tarragon, and caraway seeds in the hot stockpot until vegetables are tender, 6 to 8 minutes.

Slowly stir flour into vegetable mixture. Cook, stirring constantly, over low heat until flour is lightly browned, about 10 minutes.

Stir in beef stock, half-and-half, corned beef, sauerkraut, seasoned salt, and black pepper. Reduce heat to low and simmer until soup is heated through and slightly thickened, about 30 minutes.

Stir 2 cups Swiss cheese into soup until melted. Ladle soup into individual bowls and top with rye croutons and remaining ½ cup Swiss cheese.