Set a large pot over medium heat and add the butter and liquid smoke.

When the butter is melted, add the celery, potatoes, and 3/4 cup of the green onions. Cook for 5 minutes, until the vegetables are softened slightly. Stir in the flour to coat the vegetables, then add garlic and cook for an additional 30 seconds.

Stir in the half-and-half and broth, then add the corn, thyme, salt, and black pepper.

Simmer gently for 10 minutes, or until the potatoes are fork-tender.

Remove from heat and add the shredded cheddar, stirring until its melted.

Ladle into soup bowls, garnish with the remaining scallions, and serve hot.