To make the cookie dough, stir together the butter and sugar in a medium mixing bowl until smooth. Stir in the flour, then the vanilla and chocolate chips. Form the dough into a disk about ½ inch thick, wrap in plastic wrap, and refrigerate until firm. Once firm, chop the disk of cookie dough into bite-sized pieces, then store in the freezer until ready to mix in.
To make the ice cream, combine 1 cup heavy cream, sugar and salt in a medium saucepan. Scrape the seeds from the vanilla bean into the saucepan and add the pod to the pot. Warm over medium heat, stirring, until the sugar is dissolved. Remove from the heat and add the remaining 1 cup cream, milk, and vanilla extract. Chill the mixture thoroughly in the refrigerator.
Once the ice cream mixture is chilled, remove the vanilla bean and then freeze the mixture in your ice cream maker according to the manufacturer’s instructions. Fold the pieces of the chocolate chip cookie dough into the ice cream as you remove it from the ice cream maker.
Store in a freezer safe container in the freezer.
Notes
We recommend churning the ice cream in an ice cream maker. If you don't have an ice cream maker, you can try freezing the mixture in a freezer safe container without churning. The consistency may be different though as the churning helps create the smooth and creamy texture.
Store the ice cream in the freezer for up to one month.
Vanilla ice cream and cookie dough slightly adapted from The Perfect Scoop by David Lebovitz