In a 6-quart Instant Pot, heat butter and olive oil on sauté mode. Add onions and cook, stirring constantly, for 3 to 4 minutes or until translucent. Turn off Instant Pot.
Add broccoli, carrots, broth, thyme, pepper, salt, nutmeg, cayenne, and bay leaf.
Secure lid, turn valve to Seal, and set on Manual, high pressure (or Pressure Cook), for 4 minutes. It will take about 10 minutes for it to come to pressure.
When cook time is finished, turn valve to vent to quick release pressure. Carefully remove bay leaf.
(If a smoother consistency is desired, blend with immersion blender before continuing with remaining steps).
In measuring cup, whisk together cornstarch and milk until no lumps remain.
Turn pressure cooker to Sauté and stir in milk/cornstarch mixture. Cook for 5 minutes, stirring occasionally, until soup thickens slightly. Turn Instant Pot off and gradually stir in cheese until melted. Makes 7 cups.
Notes
Shred your own cheese for best results. Pre-shredded cheese doesn't melt as well due to additives.
Broccoli cheese soup can easily be made on the stovetop in a large pan or Dutch oven.