Combine first 7 ingredients in a large saucepan; bring to a boil. Reduce heat, and simmer 10 minutes or until broccoli is tender.
Turn off the heat. Using an immersion (hand) blender, blend the soup until it's creamy. [Alternatively if you don't have a hand blender you can use a regular blender: Pour soup into a blender. Remove center piece of blender lid (to allow steam to escape); secure lid on blender. Place a clean towel over opening in blender lid (to avoid splatters). Blend until smooth. Return soup to pan.]
Stir in 1/4 cup + 1/8 cup half-and-half and 2 ounces cheese. You don't need to turn the stove back on again, the residual heat from the soup should melt the cheese.
Top evenly with remaining 1 tbsp cheese per bowl and parsley.
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