For the cookie dough: In a stand mixer fitted with the paddle attachment, cream together the butter, brown sugar, corn syrup and salt until fluffy, 1 to 2 minutes. Add the milk and vanilla and mix on medium speed until smooth. Scrape the bowl with a rubber spatula.
Add the wafer crumbs and the mini chocolate chips. Mix until a dough forms.
Line an 8-inch square cake pan with a sheet of plastic wrap, leaving an overhang on two sides. Press half of the cookie dough into the prepared pan, making it as level as possible. Using the plastic wrap, gently pull this sheet of cookie dough out of the pan, transfer to a cutting board or baking sheet and freeze with the plastic wrap attached.
Line the same pan with two 8-by-13-inch sheets of parchment paper, leaving an overhang on two sides. Press the remaining cookie dough into the prepared pan and freeze while you make your ice cream. Wash and dry the stand mixer bowl.
For the ice cream: In a blender, combine the milk, granulated sugar, milk powder and salt. Blend on high for about 30 seconds to dissolve the sugar. Add the corn syrup and vanilla and blend on high for another 10 seconds. Set aside.
In a stand mixer fitted with the whisk attachment, whip the heavy cream on medium-high speed until medium-stiff peaks form. Use a whisk to fold the milk mixture into the whipped cream. Fold in the chocolate chips.
To assemble the ice cream sandwiches: Remove both batches of cookie dough from the freezer. Spread the ice cream over the cookie dough in the cake pan. Peel the plastic wrap off of the remaining sheet of cookie dough. Gently lay the dough on the ice cream. Wrap the pan in plastic wrap and place in the back of your freezer overnight or for up to 2 days.
Use the parchment to lift the ice cream sandwiches out of the cake pan. Use a sharp knife or a serrated knife to score into 9 bars and then cut completely. Serve immediately or refreeze after cutting (see Cook's Note).
I like to cut the ice cream sandwiches and then refreeze them before serving.