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.