Buy pre-grated carrot and Swiss cheese to save time and effort.
Combine first 10 ingredients in a Dutch oven; bring to a boil over medium heat. Reduce heat, and simmer 30 minutes. Remove and discard bay leaf.
Combine cornstarch and water, stirring until smooth; stir mixture into soup. Bring to a boil; boil, stirring constantly, 1 minute. Remove from heat.
Add shredded cheese and whipping cream, stirring until cheese melts. Top each serving with toasted rye bread cubes.
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