Roast the peppers, either over the flame on your gas burner, broiled in your oven, or roasted in your oven. Once they are charred, remove to a ziploc bag, seal, and let rest for 20 minutes.
While your peppers are resting, cook your bacon in a large dutch oven or stock pot. Fry until crispy, then remove to a paper towel lined plate. Keep the bacon grease in the pot.
Add your diced onion, garlic, celery and green pepper. Saute for 6 minutes over medium heat, until they are tender and soft.
While they are sauteing, remove skin from poblano peppers with your fingers, or the back of a spoon or knife. Remove seeds and chop. Peel and chop potatoes.
Add cubed potatoes and diced poblanos to the pot, stirring to combine. Pour in chicken stock and add salt.
Bring to a boil, then cover, reduce heat and simmer for 40 minutes or until potatoes are tender.
Whisk flour into milk, and add mixture to the pot, stirring well to combine everything.
Simmer, covered, for 10 minutes.
Turn off heat and add cheese, stirring well.
Serve topped with extra cheese, green onions, and crumbled bacon pieces.