On a cutting board prepare broccoli by chopping into 1 inch pieces. Make sure to use the stalk as well - just peel and discard the tough parts and finely chop. Set aside in a medium bowl.
Dice onion and mince garlic reserving separately on your cutting board.
Heat oil in a large saucepan over medium high heat.
Add onions and cook until tender and clear approximately 5 minutes. Stir in garlic and cumin cook for another minute stirring constantly so garlic does not brown.
Add broth and broccoli and bring to a boil, reduce heat and simmer covered for approximately 15 minutes or until broccoli is soft enough to pierce easily with a fork.
Puree soup with a hand blender until desired consistency. Add pepper and salt.
Combine milk and flour with a whisk and add to the soup. (Use a mesh strainer just to make sure there are no flour lumps.)
Cook 5 minutes until slightly thick stirring every minute or so - do not boil. If soup is too thick you can add more broth.
Stir in grated cheese and continue to stir until melted. Taste and add any additional salt and pepper if needed.