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.

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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.