Stir chicken broth, carrots, chicken bouillon, bay leaves, sea salt, pepper, thyme, marjoram, and garlic powder together in a Dutch oven; bring to a boil, reduce heat to medium, and cook for 10 minutes. Add potatoes and onion; cook for 10 minutes more. Add celery; cook until all vegetables are fork tender, about 10 minutes more.
Melt butter in a saucepan over low heat. Remove from heat and whisk flour into butter until smooth. Return saucepan to medium heat; gradually add milk to butter mixture, whisking constantly, and cook until mixture thickens, 6 to 7 minutes.
Stir milk mixture into vegetable mixture; add corn, Cheddar cheese, and ham, reduce heat to low, and simmer until ham is heated through and cheese melts, 10 to 15 minutes.
Start the white sauce right after adding celery to the other vegetables; this will cut 10 minutes off the original cooking time.
For a quicker version, use canned diced potatoes, canned carrots, frozen onions, and eliminate the celery. Combine the broth, potatoes, carrot, onions and seasonings in 5-quart pot; bring to a boil, reduce heat to medium and cook for 5 minutes. Prepare white sauce while vegetables are cooking. Combine sauce, vegetables, corn, ham and cheese; reduce heat to low and simmer for 15 minutes. This will reduce the total recipe time to 40 minutes.
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