Preheat oven to 450 F
Add 1 cup of water to instant pot, lay in trivet and rest 3 heads of garlic on it, sliced side facing up. Secure lid and cook on high pressure for 5 minutes. When down, allow for 10 minute natural release followed by a quick release
While garlic is cooking, make garlic bread croutons by combining melted 4 tbsp butter, garlic better than bouillon (or garlic powder), 1 tbsp parmesan, and Italian seasoning. Place the bread on a foil-lined baking sheet and brush garlic mixture onto the bread
Take the garlic heads from instant pot and drizzle 1 tbsp olive oil on each head. Put the heads onto the same baking sheet as the bread and put into the oven for 5-10 minutes. Once the surface of the bread is toasty and browned and the garlic is also browned, remove from oven and allow to cool
Go back to the instant pot and remove the trivet, dump the water, and dry. Hit saute and adjust to the high setting. Add the remaining 2 tbsp butter and, once melted, add the onion and let cook for 2-3 minutes. Add the meat, if using, and cook for another 2-3 minutes. Remove the liner pot from the instant pot to avoid burning while we focus on the garlic again
Take each head of garlic and squeeze all of the cloves out into a bowl. Discard any skin from the garlic
Return the liner to the instant pot, deglaze, and add in garlic broth, chicken browth, lemon juice, white wine, potatoes, roasted garlic, dried thyme, and black pepper. Secure the lid, and cook on high pressure for 8 minutes. Quick release when done
While the soup is cooking, cut the toasted bread into 1 inch cubes
When the soup is done, take an immersion blender and blend everything until pureed. Add in the 1/2 cup Parmesan and heavy cream, and puree once more time
Ladle into bowls, serve with croutons and chives for garnish