Prepare a heatproof container that fits inside Instant Pot (I use Instant Pot Pyrex bowl). Spray it with a non-stick cooking spray.
Put egg and sugar in a bowl and mix with a fork until combined. Add heavy cream and vanilla and mix until combined. Add the bread cubes and carefully mix until all bread is moistened (do not overmix). Add the chocolate chips and mix until evenly distributed.
Transfer the bread pudding mixture into the container that fits inside Instant Pot. DO NOT cover the container with foil or any other cover.
Pour 1 cup water in the Instant Pot and insert the trivet (the rack that came with the Instant Pot) with the handles up. Put the container with bread pudding on top of the trivet.
Close the Instant Pot and turn the valve to a Sealing position. Press the "Pressure Cook" or "Manual" button and set the time to 10 minutes on High pressure.
When it's done cooking, quick release (QR) the steam. Serve the bread pudding warm.
If making bread pudding ahead, refrigerate until ready to eat, then warm it in a microwave before serving.