In a small bowl, whisk together the flour, cocoa powder, baking powder, and salt.
In a medium bowl, whisk together the eggs, sugar, melted butter, vanilla, and espresso. Gently whisk the dry mixture into the wet mixture. Fold in the chocolate chips. Pour the mixture into the prepared pan and cover with aluminum foil.
Pour 1 1/4 cup of water into the Instant Pot® and place the springform pan on the steam rack. Using the handles, lower the pan into the pot. Lock the lid in place and turn the valve to Sealing. Press the Pressure Cook button and set the cook time for 35 minutes at high pressure.
Let the steam release naturally for 15 minutes, then turn the valve to Venting to quick-release any residual steam. Carefully remove the lid and, using the steam rack handles, lift out the pan. Transfer to a cooling rack, remove the foil, and let cool completely.
To serve, remove the pan sides, dust the cake with cocoa powder, and cut the cake into wedges. Serve with scoops of vanillaice cream alongside.