Remove broccoli florets from stems and set aside. Trim leaves and set aside. Cut away and discard the tough outer portion of the stems. Dice the remaining cores.
Turn on a multi-functional pressure cooker (such as Instant Pot), add oil, and select Saute function. Add onion, carrot, bell pepper, garlic, and ginger; saute until fragrant, 3 to 5 minutes. Add broccoli stems and leaves; saute for 1 more minute. Stir in broccoli florets. Add turmeric and cracked pepper; stir until vegetables are coated. Turn off Saute function and add broth.
Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 15 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure using the natural-release method according to manufacturer's instructions, for 10 minutes. Release any remaining pressure carefully using the quick-release method. Unlock and remove the lid and stir.
Puree soup with an immersion blender until creamy. Stir in yogurt and serve, or cool and freeze.