Pour ¾ cup of the heavy cream into a large bowl and place a fine-mesh strainer over the top. Set aside.

In a medium saucepan, combine the remaining 1 cup heavy cream, whole milk, granulated sugar, light brown sugar, salt, and corn syrup. Warm over medium heat, stirring occasionally, until hot but not boiling.

In a small bowl, whisk the egg yolks. Slowly whisk about ½ cup of the warm milk mixture into the egg yolks to temper them. Pour the egg mixture back into the saucepan and stir to combine.

Cook over medium-low heat, stirring constantly, until the custard thickens slightly and coats the back of a spatula. If you have a thermometer, it should reach 155–160°F. Do not let the custard boil.

Carefully pour the hot custard through the strainer and into the heavy cream. Stir in the vanilla extract.

Place the mixture over an ice bath and stir every few minutes as it cools. After about 10–15 minutes, transfer the ice cream base to an airtight container and refrigerate until completely chilled, at least 4 hours but preferably overnight.

Using a hand mixer or stand mixer, beat the softened butter, brown sugar, granulated sugar, and salt until smooth and creamy. Add the vanilla and heavy cream and mix until combined.

Add the flour and mix until a soft dough forms. Stir in the mini chocolate chips.

For easy cookie dough pieces, press the dough evenly onto a small baking sheet lined with parchment or wax paper. Freeze until just firm enough to cut easily, about 30 minutes. Cut into small squares. Alternatively, roll the dough into small bite-sized balls. Keep the cookie dough pieces frozen until ready to add to the churned ice cream.

Fill the bottom of a double boiler with about 2 inches of water and bring to a boil over high heat. Reduce the heat to maintain a gentle simmer.

Place the chopped chocolate, coconut oil, and a small pinch of salt in the top pot of the double boiler. Set it over the simmering water, making sure the bottom of the bowl does not touch the water. Stir occasionally until the chocolate is completely melted and smooth.

Transfer the melted chocolate to an 8x8-inch pan lined with wax or parchment paper. Spread the chocolate into a small rectangle, covering over half of the pan. Spread it evenly while keeping it rectangular so you can cut it into even chunks later.

Freeze for about 30 minutes, or until completely firm. You can also freeze it for up to 24 hours.

Remove the chocolate from the freezer and transfer it to a cutting board. Let it sit at room temperature for 1–2 minutes to help it cut without cracking. Cut into small squares or chunks. If it starts melting too quickly, cut half at a time and keep the other half in the freezer.

Put the chocolate chunks in the freezer until you're ready to add them to the ice cream.

When ready to churn, place the mixture in your ice cream maker and churn according to the manufacturer’s instructions until thick and soft-serve.

Transfer about ⅓ of the churned ice cream to a freezer-safe container. Sprinkle with some of the cookie dough pieces and chocolate chunks, then gently stir to distribute. Repeat with another ⅓ of the ice cream and more cookie dough pieces and chocolate chunks. Add the remaining ice cream and top with additional cookie dough pieces and chocolate chunks. Use as many of the mix-ins as you’d like; you may not need all of them.

Cover and freeze for 3–4 hours, or until firm. Let the ice cream sit at room temperature for a few minutes before scooping. Enjoy!