Preheat the oven to 350°F, then line a half sheet pan with parchment paper.

Using an electric mixer or stand mixer fitted with a paddle attachment, beat together the butter, granulated sugar and brown sugar on medium-high speed until light and fluffy. Add the vanilla extract, salt and milk, then mix on low speed until incorporated. 

In a separate bowl, whisk together the flour, cocoa powder and baking soda, then add it to the mixuture and beat on low speed until combined. Don't overmix.

Transfer the batter to the parchment lined pan, then use an offset spatula to spread the batter all over to every edge, making it as even and as smooth as you can. This batter won't spread out during cooking, so it's imperative that you make it as even as possible during this step, or you'll wind up with wonky ice cream sandwiches. It can be finicky, just do the best you can. They'll be delicious no matter what.

Bake the giant sheet cookie for about 10 minutes, or until a toothpick inserted in the center comes out clean.

Allow the cookie to cool, then use a fork to prick the top in neat rows, just like the top of an old school ice cream sandwich (this step is optional).

Cut the cookie slab crosswise into 2 even halves - make sure they're as close to the same size as possible! - then trim the edges if desired to make more uniform sandwiches. Wrap each half (with the parchment still attached) tightly with plastic wrap, then freeze until solid - preferably on a sheet pan, if your freezer has the room. Having a cold work surface will help with assembly. 

Take the ice cream out of the freezer to soften about 15 minutes before you're ready to assemble.

Unwrap the cookie halves, then carefully peel the parchment from the backs. Place one half, bottom up, on the frozen sheet pan or other cold surface. Spread with ice cream, making the layer as even as you can. Place the second half over the ice cream, top-side-up. Press down gently to push the ice cream evenly between the cookie halves. Wrap with plastic wrap, then freeze until firm. 

Use a very sharp knife to trim the edges, if desired, then cut the slab into 10 individual sandwiches. First, cut down the middle lengthwise, then then cut each half into 5 even bars.

Serve immediately, or wrap each bar in plastic wrap and store in a zip-top bag, in the freezer, for up to a month.