Set the Instant Pot on the saute setting.
Once the pot has reached temperature, add the butter and minced onions and cook until the butter is melted, stirring frequently.
Stir in the flour, cook 1 minute - stirring consistently.
Pour in the broth and then add the broccoli, salt, pepper, paprika and granulated garlic.
Cover and set the lid to sealing.
Cook on manual, high pressure for 8 minutes.
Allow for a natural release. This can sometimes take 15-20 minutes. Once done and the pin drops, remove the lid.
Use an immersion blender to blend the soup to your desired consistency.
Stir in the half and half as well as the cheese before serving.