Peel onion and chop into small pieces.
Cut away the leaves of the cauliflower and some of the stem, keeping the core part. Coarsely chop cauliflower into pieces.
Turn Instant Pot or pressure cooker to SAUTE and melt the butter; then add the onion and cook 2-3 minutes.
Then add the chopped cauliflower, canned chicken broth or chicken stock, garlic powder, and salt.
Lock the lid, use the MANUAL setting and cook on HIGH PRESSURE for 5 minutes.
Quick release the pressure.
While the soup cooks, prepare the cream cheese cubes, grated sharp cheddar, and half and half. Also cook and crumble the bacon, dish up sour some sour cream and extra grated cheese, and slice the green onions for toppings.
Check to make sure the cauliflower is very tender; then turn the Instant Pot to KEEP WARM.
Use an immersion blender or food processor to puree the soup.
Check the thickness of the soup and add more stock if you want it thinner or simmer a little to reduce if it seems too thin.
Add the grated cheese and cream cheese cubes and let them melt, then stir to combine.
Add the half and half (or heavy cream or milk) heat through, and season with salt and fresh-ground black pepper.
Serve hot, with grated cheese, sour cream, crumbled bacon, and green onion to add at the table.
