Heat olive oil in a Dutch oven and add the sausage. Cook until browned while breaking it up into small pieces. Remove from the pot with a slotted spoon and set aside.
Drain all but 2 tablespoons of grease from the pot and add the chopped onions. Cook until soft (about 5 minutes.) Add the minced garlic and stir to avoid burning.
Add the carton of chicken broth and the cauliflower florets to the pot. Season with salt and pepper and stir to combine. Simmer about 15 minutes or until the cauliflower is soft.
Remove the soup from the heat and puree by either using a regular blender (work in batches) or an immersion blender.
Return the soup to the heat, add the half and half, and bring to a gentle simmer. Stir in the cooked sausage.
Taste to adjust seasoning, and remove from the heat. Serve warm and garnish with grated cheddar cheese and chopped fresh parsley.