The Smoothest and Best Ever Dark Chocolate Custard Ice Cream

Name: The Smoothest and Best Ever Dark Chocolate Custard Ice Cream
Prep time: 1 h
Total time: 1 h
Cuisine: American, Southern
Ingredients: ⅓ cup unsweetened cocoa powder ((good quality, see notes)); 1 cup sugar ((divided in half)); 2 cups whole milk; 2 ⅓ cups heavy whipping cream; 2 large eggs; 4 egg yolks ((do not add whites)); 4 oz semisweet chocolate ((coarsely chopped or chips)); 1 tsp vanilla extract