Lightly oil 4-quart Dutch oven (or large saucepan) and heat over medium heat until hot.
Add onion and celery. Cook and stir for 3 minutes, until crisp-tender.
Addvegetable stock and salt & bring to a boil over high heat. (NOTE:You may wish to add the salt at the very end after tasting the chowder.That's what we did, and depending on your stock, corn choice, etc. youmay not need any salt at all.)
Add potatoes and carrot.Reduce heat to medium-low. Then simmer, covered for 10 minutes (oruntil potatoes and carrot are tender).
Stir in corn, beans, pepper, and poppy seeds. Simmer -- again, covered -- for 10 minutes (or until heated through).
Whisk milk into cornstarch in a medium bowl until smooth. Stir into vegetable mixture.
Simmer -- uncovered -- until thickened.