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In a 4-quart dutch-oven, heat olive oil over medium heat.
Add onions and carrots, and sauté for 4-5 minutes, stirring occasionally, until the onions are soft.
Stir in the garlic and cook for additional 30 seconds.
Stir in the flour and cook for 1 minute while stirring. Add the bay leaf, mustard, nutmeg, salt, pepper, and then gradually whisk in the milk until smooth. Add the vegetable stock and bring to a simmer, then simmer for 3-4 minutes or until slightly thickened.
Add broccoli, reduce heat to medium-low and simmer, uncovered, for 8-10 minutes or until tender.
Turn off the heat, discard the bay leaf, and gradually stir in cheese. Taste for salt and pepper.
Serve immediately, topped with extra cheese and cayenne pepper, if desired.