Preheat the oven to 450 degrees F. Pierce the potatoes all over with a fork. Microwave until cooked through, 8 to 10 minutes. Cook the bacon in a large pot or Dutch oven over medium heat, stirring, until crisp, about 8 minutes. Remove to a paper towel-lined plate using a slotted spoon. Add the onion to the pot with the drippings; cook, stirring occasionally, until softened, 5 minutes.
Meanwhile, coat a baking sheet with cooking spray. Quarter the potatoes lengthwise and scoop out most of the flesh; set aside. Arrange the potatoes skin-side up on the prepared baking sheet; coat with cooking spray. Bake until golden, 15 minutes.
Meanwhile, add the potato flesh, 6 cups water, 1 teaspoon salt and a few grinds of pepper to the pot with the onion and stir to combine. Bring to a boil. Add the broccoli and reduce the heat to maintain a simmer; cook until the broccoli is tender, about 8 minutes. Working in small batches, puree in a blender. Return to the pot and stir in the half-and-half; season with salt and pepper.
Remove the potato skins from the oven; flip and top with the cheese. Continue baking until bubbling and golden. Top each serving of soup with the bacon and serve with the potato skins.
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.