Add corn, potatoes, onion, celery, garlic, broth, salt, pepper, and smoked paprika to a 6-quart or larger slow cooker. Stir well.
Cover and cook on low for 5 to 6 hours or on high for 3 to 4 hours, until potatoes are fork-tender.
Use a potato masher to mash some of the potatoes directly in the slow cooker for a thicker chowder, leaving plenty of chunks.
In a small bowl, whisk milk, heavy cream, and cornstarch until smooth. Stir the mixture into the chowder.
Add cheddar cheese if using. Cover and cook on high for 15 to 20 minutes, until thickened and the cheese is melted.
Taste and adjust seasoning. Serve with bacon, green onions, and extra cheddar if desired.