Freeze your ice cream bowl (from an ice cream maker) overnight.
To a medium sized pot on medium heat add your heavy cream, milk, sugar and eggs and whisk them together. Whisk continuously and cook for about 5 minutes, or till the mixture has thickened slightly and has a custard-like color (You can also check it with a thermometer and it should be about 170).
Remove your pot from the stove. Add your vanilla extract and whisk it in.
Pour into a bowl, cover, and place in the fridge for at least several hours or overnight (the ice cream base needs to be completely chilled).
About an hour prior to adding the ice cream base to the ice cream machine, make your gluten-free cookie dough bits.
To a medium mixing bowl, add your butter, sugar, and brown sugar and mix together till creamed. Add your vanilla and stir till combined.
To the same bowl, add your flour and salt and stir together till you have a thick cookie dough. If your cookie dough is too thick, add 1-2 teaspoons of milk (or until it reaches the desired consistency).
Add your mini chocolate chips and fold them into the cookie dough.
Prepare a small pan with parchment paper. Using a 1/2 teaspoon, scoop out bits of cookie dough and place them onto the pan. I recommend using a mini spatula to easily remove the dough from the teaspoon. After you've scooped all of the dough out, you can roll each cookie dough scoop into a smooth ball.
Sprinkle 1/3 cup of your chocolate chips around the pan. Place the pan in the freezer for at least an hour.
Be prepared to move quickly now; the colder the ice cream stays, the better it's texture will be.
Assemble your ice cream maker with the frozen bowl. Turn it on and pour your vanilla ice cream base into it. Let it run according to your ice cream maker instructions (mine is only 10-15 minutes).
After the minimum process time, taste test your ice cream consistency (it should be like soft serve and taste delicious). Then remove your cookie dough chunks and chocolate chips and add them to your ice cream base. Contine to process for about a minute, or till they're thoroughly mixed in.
Turn your ice cream maker off and quickly scoop your ice cream into a freezer safe container. Cover and place in the freezer.
Let it freeze for several hours, for it to be scoopable, hard ice cream.
After several hours: scoop, serve, and devour!
Stored in an airtight container in the freezer, this ice cream should last about 1-2 weeks.