Combine the potatoes, celery, onion, bouillon cubes and water in a stockpot. Bring to a boil, then cook over medium heat until potatoes are tender, about 10 to 15 minutes. Stir in white and black pepper & salt to taste.

In a separate saucepan, melt butter over medium-low heat. Whisk in flour with a fork, and cook, stirring constantly until thick, about 1 minute. Slowly stir in milk, whisking out any lumps. Continue stirring over medium-low heat until thick.

Stir the milk mixture into the stockpot, and cook soup until heated through. Serve immediately. Top with shredded cheddar cheese, bacon and green onions if desired.