Add sugar and cocoa powder to a bowl and mix together, making sure to break up any clumps in the cocoa powder. You may want to sift in the cocoa to remove any clumps. Then add cream cheese and blend until smooth with a hand mixer.
In a microwave safe bowl, combine chocolate chips and heavy cream. Microwave chips and heavy cream for 25 seconds, then whisk until completely smooth. If chips are not melted after one minute of whisking, microwave for 10 second intervals, stirring in between, until smooth.
Let chocolate mixture cool until warm, not hot, then fold into cream cheese mixture until completely combined.
Add eggs (one at a time) and vanilla and mix until just combined. Tap bowl against counter top several times until air bubbles rise to surface. Burst bubbles with fork or toothpick.
Remove cheesecake crust from freezer and pour batter into pan. Add 1 1/2 cups water and 3-inch trivet to Instant Pot. Cover cheesecake with foil, and place on trivet. Cook for 40 minutes at high pressure, then allow a natural pressure release.
Once pressure is released, turn off Instant Pot and carefully remove cheesecake. Remove foil and allow cheesecake to cool for one hour or until room temperature. Once cool, carefully run a paring knife around the edge of the cheesecake to separate from pan. Refrigerate for at least 6 hours, preferably overnight.
Carefully push cheesecake up from push pan by placing center of push pan on a can or glass and pushing edges down. If using springform pan, gently remove outer edge of pan. Then serve and enjoy.