Cream together the unsalted butter, granulated sugar, and light brown sugar until light and fluffy, then mix in the vanilla extract. In a separate bowl, combine all-purpose flour, baking powder, and salt. Fold the dry ingredients into the buttery mixture, then gently add the mini chocolate chips. Chill the dough for 30 minutes.

In a medium saucepan, combine heavy cream, whole milk, granulated sugar, and a pinch of salt over medium heat. Stir until the sugar dissolves, about 5 minutes. Remove from heat and stir in the vanilla extract. Cool to room temperature and refrigerate for at least 4 hours.

Pour the chilled ice cream base into an ice cream maker and churn according to the manufacturer's instructions, about 20-25 minutes.

Chop the chilled cookie dough into small chunks and add to the ice cream maker during the last few minutes of churning.

Transfer the ice cream into an airtight container, smooth the top, and freeze for 2-3 hours until firm. Let sit at room temperature for a few minutes if too hard to scoop.