In a small saucepan, warm the half and half and vanilla over low heat for 15 minutes.
In a large bowl, whisk the eggs and sugar until well combined. Set aside.
After 10 minutes of warming the half and half stir in the hot cocoa. Whisk well until the instant hot cocoa is fully combined and dissolved. Continue to cook for 5 minutes.
While whisking the egg and sugar mixture, add a spoonful of warm cocoa half and half. Continue to whisk to prevent scrambling of the eggs. Continue this process three more times until the custard is warmed.
In a steady stream pour the remaining cocoa half and half into the custard, whisking continually.
Place the brioche into a 7-8 ounce porcelain ramekin. Pour the custard over the bread. Be sure that the tops of the bread are coated by the custard.
Add the water to the Instant Pot and place the steam rack into the Instant Pot.
Place the ramekin onto the steam rack. Secure the lid onto the Instant Pot. Using the manual setting, cook on high pressure for 20 minutes. After the 20 minutes, turn off the Instant Pot and let the pressure release naturally for 20 minutes. After 20 minutes release any remaining pressure.
Remove the bread pudding. Let cool for 5 minutes.
Top with chocolate syrup, marshmallows and caramel corn.