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1. Add chicken broth, diced potatoes, broccoli pieces, and diced carrots to stockpot.
2. Bring to a boil over medium-high heat.
3. Reduce heat to low. Cover stockpot with lid. Simmer 20 minutes.
4. Add cornstarch and half-and-half to small bowl.
5. Stir cornstarch into soup mixture.
6. Add 1 cheese slice at a time to soup. Stir continuously until each slice melts.
7. Serve hot.
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