Melt the butter in a soup pot over medium heat. Add the onion and cauliflower and cook, stirring occasionally, until the onion is softened but not browned, about 10 minutes. Add the chicken broth and bring to a boil. Reduce the heat and simmer until the cauliflower is softened, about 20 minutes.
Meanwhile, in a nonstick skillet over medium heat, cook the bacon until crisp; drain on a paper towellined plate. (Do not clean the skillet.) Cut the bread on the diagonal into four 1-inch-thick slices. Place the bread in the skillet and cook until golden on the bottom, 1 to 2 minutes. Flip and top each slice with 2 pieces of bacon and a handful of cheese. Cover until the cheese melts, about 1 minute.
Puree the soup in batches in a blender until smooth. Season to taste with salt and serve with the bacon toasts.