Set Instant Pot to saute.
Melt butter in Instant Pot. Add onions and carrots. Cook, stirring occasionally just until starting to soften. Stir in garlic and cook just 30 seconds more.
Pour in broth. Add salt, pepper and then broccoli. Cancel saute function.
Cover, seal and set to high/manual pressure for 1 minute.
When 1 minute is up. Carefully, quick release the pressure.
Using a slotted spoon, remove approximately half of the broccoli. Set aside in a bowl.
Blend the soup mixture with an immersion blender. (See notes if no immersion blender)
Set the Instant Pot back to the saute function.
Stir together cornstarch and cold water and add to soup. Allow the soup to thicken, cooking 2-3 minutes. Stir in milk and heavy cream. Cook just 1 minute more. Cancel saute function.
Stir in cheese, a little at a time to avoid clumping. Stir reserved broccoli back into soup.
Serve warm.