In Dutch oven, melt butter over medium heat; cook ham, onion, carrot, celery, garlic and jalapeño pepper, stirring occasionally, until softened, about 10 minutes.
In small bowl, whisk together flour, chili powder, oregano and pepper; add to vegetables and cook, stirring, for 1 minute. Whisk in chicken stock. Add potatoes and bring to boil; reduce heat, cover and simmer until potatoes are tender, about 7 minutes.
Stir in milk and corn; simmer, covered, until corn is tender, about 5 minutes. (Make-ahead: Let cool for 30 minutes; refrigerate, uncovered, until cold. Refrigerate in airtight container for up to 24 hours.) Ladle into bowls; sprinkle with cheese and coriander.