Preheat oven to 350ºF and line an 18x13" (half-sheepan with parchment paper.
In a large bowl, whisk together flour, sugar, cocoa, baking soda and salt. In a separate large bowl, whisk egg, then whisk in buttermilk, oil and vanilla. Scrape the egg mixture into the flour mixture and gently fold together until no dry flour remains. Do not overmix.
Dollop the cookie mixture onto the prepared baking pan. Use a metal spatula to smooth the batter evenly over the whole pan. It is a thick, sticky batter. You'll need to run your spatula under hot water, dry it off, then spray with nonstick spray (or use a paper towel dipped in oito grease it. Anytime the batter starts to catch on the spatula rather than glide smoothly in the pan, repeat the hot water and greasing procedure. You'll need to do it several times.
Bake for 7 minutes, until set but still a bit shiny in spots. Cool to room temperature, slice the slab in half while still in the pan, then transfer the whole thing to the freezer until firm, about 30 minutes.
Place one half of the frozen cookie slab pretty-side down on a work surface. Scoop the ice cream over top (or I find it easier to cut open the carton with scissors and then slice the hard ice cream into slabs). Use a knife or metal spatula to firmly press the ice cream down to evenly cover the bottom cookie. Place the second cookie slab, pretty side up, on top and transfer the whole thing back to the freezer until ice cream is very solid again.
Use a sharp knife dipped in hot water to slice into equal-sized ice cream sandwiches. Freeze individual sandwiches in a single layer on a baking sheet until hard, then you can wrap them individually in plastic wrap or parchment paper tied with kitchen string and store up to a month.