Keep in mind that during this whole process you don't want the soup to boil. (This can cause it to separate and ruin the texture.)
Saute onions in butter in a large saucepan or Dutch oven.
Cube cream cheese.
Add cubed cream cheese and heavy cream or half and half to green onions.
Stir over low heat until the cream cheese is melted.
Stir in chicken broth.
Add half of the chopped broccoli.
Process soup with an immersion blender or in a countertop blender until smooth.
Stir in lemon juice and seasonings.
Add remaining chopped broccoli.
Cook over low heat until frozen broccoli is tender.
Garnish each bowl with toasted almonds and fresh herbs if desired.