Prepare the Ice Cream Custard: Combine the chocolate and cream in a large, heatproof bowl set over a saucepan of simmering water. Stir until the chocolate is melted, then remove the bowl from the saucepan. Set it aside with a mesh strainer over the top.
Warm the milk, sugar and salt in a medium saucepan over medium-low heat, stirring occasionally, until the sugar is dissolved. In a separate medium bowl, whisk together the egg yolks. Slowly pour the warm milk mixture into the egg yolks, whisking constantly, then scrape the warmed egg yolks back into the saucepan.
Stir the mixture constantly over medium heat with a heatproof spatula, scraping the bottom as you stir, until the mixture thickens and coats the back of the spatula (it should reach 170-175 degrees F on an instant-read thermometer). Pour the custard through the strainer into the chocolate mixture and stir in the vanilla extract. Place the bowl in an ice bath and stir occasionally until the mixture has cooled to room temperature. Cover and chill in the refrigerator overnight.
Make the Chocolate Chip Cookie Dough: Combine the butter and both sugars in a mixing bowl and beat on medium speed until light and fluffy, 2 to 3 minutes. Add the cream, vanilla and salt, and mix for another minute or so, until combined. Scrape the sides of the bowl, then reduce the mixer speed to low and gradually add the flour, mixing just until incorporated. Using a rubber spatula, stir in the chocolate chips. Refrigerate for at least 30 minutes, or up to 2 days.
Churn the Ice Cream: Just before churning the ice cream, scoop the cookie dough into ½-teaspoon to 1 teaspoon-sized balls and place on a plate or parchment-lined baking sheet and place in the freezer. Churn the ice cream according to the manufacturer's instructions. When finished churning, fold in the chunks of cookie dough and transfer to an airtight container. Freeze until firm, at least 4 hours.
Note: If you prefer a vanilla ice cream base for your chocolate chip cookie dough ice cream, just use the same method as outlined above, substituting my favorite vanilla ice cream for the chocolate.Nutritional values are based on the whole recipe