Select the sauté function on the Instant Pot.
Once hot, add butter, and crushed garlic. Sauté about one minute, or until garlic begins to brown.
Add broccoli, potatoes, and broth. Season with extra salt and pepper. Secure the lid and select manual. Cook at high pressure for 5 minutes.
Once cooking is complete, select cancel and use the natural release for 10 minutes. Remove any remaining steam.
If using bacon, cook the bacon until desired crispiness. Set aside to cool.
Add the half and half and 1/2 cup of cheddar cheese. Blend with an immersion blender until smooth, or blend in batches in a large blender. If you want a thinner soup, add more broth. Add salt and pepper to taste.
Serve hot with remaining cheddar and bacon (if using).