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1. Heat oil in a large pot over medium-high heat. Add onion and carrots and sauté for 5 minutes, stirring occasionally, until the onion is see-through. Stir in garlic and sauté for an additional 1-2 minutes, stirring occasionally, until fragrant. Stir in flour and cook for an additional 1 minute, stirring occasionally.
2. Stir in stock until evenly combined. Stir in milk and mustard until combined. Continue cooking until soup is hot, but not boiling. Reduce heat to medium and add in broccoli and cheese, stirring until combined. Continue cooking for 2-4 more minutes, or until broccoli is tender.
3. Garnish with extra cheese and serve hot.