On the Instant Pot, turn on and set the sauté function to normal. Once it is hot, add the oil and let the oil heat up for about 30 seconds. Then add the onions and carrots and sauté until the onions are translucent, make sure to stir frequently, so the onions do not stick and burn (about 4-5 minutes). If the onions or carrots start to stick, add a few dashes of water to the pot and stir.
Next, add the garlic and cook for about 30 seconds and then turn off the Instant Pot.
Add the broccoli florets, turmeric, bay leaves, and vegetable stock. Close the lid and turn the valve to sealed. Set the IP to high pressure and cook for 6 minutes. Once it is done, throw a towel over the valve/vent and turn the valve to release for a quick release of the pressure. Once the lid is unlocked, slowly open the lid away from you so you do not burn yourself.
For the cheese sauce, add all of the ingredients into a high speeder blender and blend until very smooth. You can use more milk if you prefer a thinner sauce consistency.
Remove the bay leaves. Now you will need to puree the soup mixture. You can do so by adding the mixture to a blender (this can be done in batches) or using a small hand immersion blender. I prefer using a hand blender because I find it doesn't incorporate a lot of air like a blender does (plus I don't have to move the soup out of the pot to blend).
After the soup is pureed, add the cheese sauce and stir to combine. Add salt & pepper to taste.
You can top it with a little bit of shredded vegan cheese and serve with crusty bread or crackers.