Turn on a multi-functional pressure cooker (such as Instant Pot®) and select Saute function. Add butter and melt. Stir in onion and garlic; cook until onion is soft and translucent, about 5 minutes. Turn off Saute function.
Add corn, potatoes, vegetable broth, thyme, paprika, salt, and pepper to the pot; stir to combine. 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, about 15 minutes. Release any remaining pressure carefully using the quick-release method according to manufacturer’s instructions. Unlock and remove the lid. Remove 1 cup of potatoes and corn to a bowl. Mash with a fork and return to the pot.
Select Saute function again and pour in heavy cream. Cook until soup has thickened to desired consistency.
Frozen corn may be substituted for fresh, if desired.
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