Heat the butter in a large saucepan over medium-hih heat. Add the onions, carrots, and celery. Cook until tender 8-10 minutes.
Mix in the garlic, thyme and flour and cook until flour is lightly browned, about 2-3 minutes.
Slowly stir in broth deg-lazing the pan and you go. Add the half and half and potatoes, bringing to a boil. Reduce heat and simmer until potatoes are tender 10 to 12 minutes.
Add the ham and corn, cook until heated and season with salt and pepper.