In a large pot, sauté the scallions in the olive oil over medium heat until soft. Add the garlic and sauté for another 30 seconds.

Add the chives, broccoli, and broth. Bring just to a boil, then simmer gently for 25 to 30 minutes until the broccoli is tender.

Use an immersion blender to puree the soup. Stir in the milk and salt, and taste the soup to see if it needs additional seasoning.

Serve warm, and garnish with grated cheese if desired.