Select saute mode and add olive oil to the instant pot, once hot add the mushroom and saute for about 5 to 6 minutes. Add the leek and garlic and continue cooking for another 3 minutes. Cancel saute mode.
Add the carrots, celery, rice, broth, dried thyme, bay leaves, salt, and pepper. Stir.
Place the lid on the instant pot, seal the valve, select manual high pressure, and cook for 15 minutes. (it will take about 20 minutes for the pressure to rise and start cooking)
Once the soup is cooked, let the pressure release naturally.
Open the lid carefully, add the heavy cream and stir to combine everything.
Serve in a bowl, and garnish with fresh thyme if desired.