Chop up 8 ounces of baker's chocolate into small pieces. Add to a microwave-safe bowl and set aside for now.
Combine the cornstarch and water, stirring until smooth. Set aside.
In a medium saucepan, combine the milk, coconut milk, salt, and sugar. Heat over medium-high heat, stirring frequently, bring almost to a boil (you should start to see bubbles, but do not allow it to come to a full boil).
Immediately remove it from the heat. Give the cornstarch one more quick stir, then pour it slowly into the coconut milk mixture, whisking as you pour. Return the pan to the stovetop and turn the heat down to medium-low. Continually whisk for 15 minutes. The mixture should thicken to the consistency of thick yogurt. Be sure to cook the haupia for the full 15 minutes; even if it thickens up before then time is up!
Remove from the heat and stir in the coconut extract. Allow it to cool for a few minutes.
While the haupia cools slightly, microwave the chopped-up chocolate in 15-20 second intervals, stirring between intervals. The chocolate is done when only a few small chunks of chocolate remain (stopping at this point prevents scorching the chocolate). Then stir the chocolate until it's completely melted and smooth.
Add 3 cups of haupia to the melted chocolate. Stir until thoroughly combined, and you do not see any white streaks. Pour the chocolate haupia onto the crust, smoothing it into a flat, even layer. Place the pan in the refrigerator for 5 to 10 minutes to allow the chocolate layer to set up a bit.
Meanwhile, whisk the remaining haupia to prevent lumps from forming. After the chocolate layer has chilled for 5 to 10 minutes, remove it from the refrigerator and pour the remaining haupia on top of the chocolate layer. Smooth the haupia into an even layer.
Cover the pan tightly with foil and return it to the refrigerator and allow it to chill for at least 4 hours or overnight.
To serve, pull up on the parchment paper overhang and remove the bars from the pan. Cut to the desired size, wiping the knife after each cut. Add cool whip or whipped cream and a little shaved chocolate.