In a stand mixer combine the whole milk and sugar. Whisk on high speed until sugar dissolves. (always start slow so you don't splash liquid all over the place)
Add vanilla. Give it a quick whir.
Add the heavy cream and salt to the mixer. Whisk until it becomes fluffy and almost whipped cream in texture.
Cover the bowl and pop in the fridge for at least an hour, or overnight.
Remove and transfer to an ice cream maker.
Turn on and churn for about 10 minutes, just until it starts to thicken and harden a bit.
Now toss in the broken bits of cookie dough. Keep whisking until they mix into the ice cream.
Stop the machine and remove the bowl. Cover and pop in the freezer until ready for it. I find it takes about 2 to 4 hours to harden.
If you want to make it easier to form the ice cream sandwiches you can forgo freezing it in the machine. Instead pop it in a shallow 9 x 13 inch casserole dish lined with parchment. Smooth it out and pop in the freezer overnight.
Now when you take it out you can cut the ice cream with a biscuit cutter or a glass that's the same size of the cookies you're using.
Cut your ice cream and place it between two cookies. Press together.
Eat right away or wrap in plastic wrap till you need them.
Serve with a big old cookie dough smile!