1. Heat the oil in a large saucepan over medium heat. Add the onion and red pepper (if using) and cook, stirring occasionally, until the onion is soft, 4-6 mins.
2. Add the broth, broccoli, potato, 2 cups water, 1/2 tsp salt, and 1/4 tsp black pepper to the saucepan and bring to a boil. Reduce heat and simmer, covered, until the vegetable are very tender, 18 to 20 mins.
3. In a blender, working in batches, puree the soup until smooth, adjusting the consistency with water as necessary. (Alternatively, use a handheld immersion blender in the saucepan). Top with the CHeddar and bagel chips, if desired, before serving.
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