Heat oil in a Dutch oven over medium heat. Add onions; sauté 2 minutes or until tender. Add corn and next 7 ingredients (corn through thyme sprig); bring to a boil. Reduce heat; simmer 30 minutes or until potato is tender.
Combine cornstarch and evaporated milk in a small bowl; stir with a whisk.
Add cornstarch mixture to soup; simmer 5 minutes or until thick, stirring occasionally. Add mushrooms and crab; remove thyme sprig. Ladle into soup bowls; sprinkle with chives, if desired.