Heat the oil in a large sauce pan over medium-high heat, add the onions, carrots and celery and cook until tender, about 8-10 minutes.Mix in the garlic, thyme and flour and cook until the flour is lightly browned, about 2-3 minutes.Slowly stir in the broth, deglazing the pan as you go, add the milk and potatoes, bring to a boil, reduce the heat and simmer until the potatoes are tender, about 10-12 minutes.Add the ham and corn, cook until heated and season with salt and pepper.