In a medium saucepan, warm half and half, granulated sugar, brown sugar and salt over medium heat.
Beat egg yolks in a small mixing bowl, add ½ cup of the warm half and half mixture to the egg yolks and whisk to combine. Once combined, pour the mixture into to the half and half on the stovetop.
Cook over medium-low heat stirring constantly until the mixture thickens slightly and just barely coats the back of a spatula.
Put the heavy cream into a bowl, then place a fine mesh strainer on top of the bowl.
Strain the custard into the heavy cream. Discard the residue on the strainer.
Add vanilla extract and stir to combine.
Transfer to an airtight container and cool completely in the fridge (preferably overnight).
Line a baking sheet with wax paper, set aside.
In a small bowl, mix together the flour, baking soda, baking powder and sea salt. Set aside.
In a medium bowl, cream together butter, granulated sugar and brown sugar with a hand-held mixer (or standing mixer) until well combined (about 60 seconds). Be sure to start on low speed and increase it as the ingredients begin to stick together.
Add 4 Tablespoons milk and vanilla extract and beat on medium speed until combined.
Add dry ingredients and mix, starting on low speed and increasing to medium-high, until all ingredients are combined.
Add mini chocolate chips and stir until evenly distributed.
Spread the cookie dough evenly on the prepared baking sheet, then place it in the freezer to harden.
One hardened, cut into chunks with a sharp knife. Then keep frozen until ready to add to the ice cream.
Once the vanilla ice cream is completely chilled, turn an ice cream make on and pour mixture into it while it’s turning. Churn until thick and frozen.
Transfer to a freezer-friendly container.
Add the cookie dough pieces to the churned ice cream and stir until evenly combined.
Transfer to the freezer to freeze until hardened (3-4 hours).
Remove from the freezer 3-5 minutes before serving to soften. Then scoop and enjoy.
