Line a 9x13 inch sheet pan with plastic wrap. Drop soft 1½ quart ice cream by the scoop over pan, then spread to edges. Cover with plastic wrap or parchment paper, and freeze for up to 1 hour.
Preheat oven to 350˚F and line two 9x13 inch pans with parchment paper.
Using a stand mixer and mixing bowl, add ½ cup butter with ¼ cup sugar and ½ cup brown sugar Beat until fluffy.
Add 1 large egg, 1 teaspoon vanilla, and ½ teaspoon kosher salt. Blend until light in color.
Slowly add 1¼ cup flour, ½ cup cocoa, ½ teaspoon baking soda, and ½ teaspoon espresso powder (if using) to the sugar mixture. Blend for 1 minute until smooth. Warm ½ cup milk for about 40 seconds in the microwave, add to the mixture, and blend for 1 minute more. The batter will be thick.
On two parchment lined pans, drop dough by spoonful. Spread dough to edges as evenly as possible.
Bake for 8 minutes. Remove from oven and pierce randomly with a fork or leave plain. Cool completely on a wire rack. Transfer to freezer for 2 hours or overnight.
Assembly
Once ice cream and cookie layers are frozen, remove any plastic or parchment paper. Layer cookie, ice cream, and second cookie.
Press down gently. Set back into freezer until firm enough to cut without squishing out the ice cream
Cut into 10 rectangles and serve immediately. Or wrap each in plastic and store in freezer.
Notes
1.5 quart ice cream is equivalent to 1.4 L
Store assembled ice cream sandwiches in the freezer for up to 2 months.
Wrap individually for grab and go treats, and place in a freezer friendly container or bag to prevent freezer burn.
If stacking, separate layers with parchment paper to keep them from sticking.