Line the base of a 7-inch round springform pan with an 8-inch round of parchment paper. Secure the collar on the springform pan, closing it onto the base so the parchment round is clamped in. Lightly grease the sides of the pan with butter or nonstick cooking spray.
Put the melted butter in a large bowl. One at a time, whisk in the eggs, then the brown sugar, coffee, vanilla, and salt until combined. Add the flour and cocoa powder and whisk just until the dry ingredients are fully incorporated. Fold in the chocolate chips and walnuts.
Pour the batter into the prepared pan. Tap the pan firmly against the countertop a few times to remove any air bubbles in the batter. Cover the pan tightly with aluminum foil. Place the pan on a long-handled silicone steam rack.
Pour 1 1/2 cups water into the Instant Pot. Holding the handles of the steam rack, lift the pan and lower it into the pot.
Secure the lid and set the Pressure Release to Sealing. Select the Cake, Pressure Cook, or Manual setting and set the cooking time for 35 minutes at high pressure. (The pot will take about 10 minutes to come up to pressure before the cooking program begins.)
When the cooking program ends, let the pressure release naturally for 10 minutes, then move the Pressure Release to Venting to release any remaining steam. Open the pot and, wearing heat-resistant mitts, grab the handles of the steam rack, lift the pan out of the pot, and set the pan on a cooling rack.
Remove the foil from the pan, being careful not to get burned by the steam. Let the cake cool for about 20 minutes, until warm, or cool to room temperature.
Unclasp the collar on the pan and lift it off, then use the parchment border to tug the cake off the base of the pan and onto a plate. Slice the cake into wedges and serve.