Melt butter in a large saucepan. Add the shallots and celery and saute until almost done about 4 min. Next in goes the garlic and it is sauteed for another minute. Then, add the flour and cook for 1 min. stirring. Add in the broth slowly and whisk constantly until all is incorporated and smooth.

Add in the potatoes, thyme, salt, and pepper, bring to a simmer and cover. Cook for 15 min. or until potatoes are fork-tender.

Add in the milk and bring back up to a simmer. Add in the cheese and stir. Season again if needed with salt and pepper. Serve, topping each bowl with some green onion.