Lightly score hot dog skins from end to end on 4 sides. This helps keep them flat when they cook. Slice into 1/2-inch rounds.

Melt butter in a large pot over medium heat. Add onions, poblano pepper, celery, and cayenne pepper. Season with salt and pepper. Cook and stir until vegetables are soft and onions are translucent, 5 to 7 minutes.

Stir in hot dog slices and cook until heated through and fat from hot dogs mixes with butter, about 3 minutes. Add brown sugar, ketchup, mustard, and Worcestershire sauce; pour in chicken broth. Stir in beans. Increase heat to bring mixture to a simmer; reduce heat to low and cook until flavors mix, about 30 minutes. While beans are cooking, use a wooden spoon to crush some of them against the side of the pot to help thicken the stew. If mixture gets too thick, add more broth.

Just before serving, stir in chopped green onions.