Cook the bacon in a large Dutch oven over medium-high heat, stirring occasionally, until crisp, about 10 minutes. Transfer to paper towels with a slotted spoon; set aside to drain. Add the scallions and celery to the drippings in the pot and cook until slightly softened, about 2 minutes. Add the flour and cook, stirring, until incorporated. Add the broccoli, chicken broth, 3 cups water, 1 teaspoon salt and a few grinds of pepper. Increase the heat to high and bring to a boil. Add the edamame, reduce the heat to medium low and simmer until slightly thickened, about 10 minutes. Working in batches, transfer the soup to a blender and puree until smooth; return to the pot. Stir in the half-and-half and simmer 5 minutes. Stir in the cheese and continue to cook, stirring, until the soup thickens, about 5 more minutes. Season with salt and pepper. Divide among bowls and top with the bacon.