IN a small bowl whisk together 3/4 cup of the sugar and the cocoa powder.
Pour 2 cups whole milk into a medium saucepan and whisk in the sugar/cocoa mixture. Heat on medium until the mixture reaches 185 degrees on an instant-read thermometer. Once you reach 185 degrees, continue to cook the mixture for 5 minutes, stirring constantly, but do not boil.
Remove from the heat and add the chocolate chips. Stir until all the chocolate has melted. Set aside.
In a small mixing bowl, whisk the egg yolks with the remaining 1/4 cup sugar until slightly thick and foamy. Temper the eggs by whisking in a small amount of the hot chocolate mixture to the eggs, while whisking constantly. If you've never tempered eggs before, there's nothing to it. Basically you're trying to warm the eggs without cooking them. To do this you want to whisk in small amounts of the hot mixture until you have added about 1/2 the hot chocolate. I use a small ladle to drizzle the chocolate into the eggs and whisk constantly until blended. Then add a little more, and so on. The egg mixture should be thick and smooth with no lumps.
Pour the tempered egg mixture into the saucepan with the remaining chocolate and blend. Using a wooden spoon constantly stir the mixture over medium heat until it reaches 185 degrees again on the instant-read thermometer. Do not allow the mixture to boil. Remove from the heat and set aside. Place a large bowl in your sink and fill it with ice. Place a stainless-steel or glass bowl in the ice bath and add the heavy cream. Set a fine mesh strainer on top of the bowl and pour the hot chocolate custard through the sieve into the cold cream. Add the vanilla extract and stir until completely blended.
Cool the mixture by stirring every 5 minutes while over the ice bath. After about 30 minutes, cover the bowl with plastic wrap and refrigerate overnight.
Process according to your ice cream maker instructions. Freeze the gelato in a sealed container until ready to serve. Enjoy!