Place a 4 quart pot over medium-high heat and add oil.
When it's hot, add onions and sauté until they have softened.
Add garlic and continue to sauté for another minute. Add stock, grated potatoes and broccoli stems.
Season with salt and pepper and simmer until they are tender and potatoes have broken down.
Add nutmeg and adjust seasoning and puree with an immersion blender or in a food processor.
Reheat soup prior to serving and add reserved broccoli florets and cheddar cheese.
Simmer for about 5 minutes, until cheese has melted and florets are tender and bright green.
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