Turn on a multi-functional pressure cooker (such as Instant Pot(R)), select Saute function, and allow to heat. Add olive oil and onion; saute until soft, about 3 minutes. Add garlic and saute another minute. Add broth, cauliflower, and butternut squash. Close and lock the lid; set vent to seal. Select high pressure according to manufacturer's instructions; set timer for 6 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Unlock and remove lid.
Stir curry powder and salt into soup in the pressure cooker. Blend soup to desired texture using an immersion blender. Stir in shredded mozzarella and Cheddar cheese blend and serve immediately.