Melt butter in a Dutch oven over medium heat. Add onion and celery; saute 3 minutes. Add garlic and bay leaf; sauté 2 minutes. Add milk, thyme, salt, pepper, chopped loaded potatoes, and broth; bring to a boil. Reduce heat; simmer 10 minutes. Ladle soup into 4 bowls; top each serving with 1 tablespoon green onions.