Preheat oven to 350F. Line a 9x13 baking pan with parchment paper, letting a little bit overhang the sides. Set aside.
In a small saucepan over medium heat, melt butter and chocolate until smooth. Remove from heat and set aside to cool.
In a large bowl, whisk eggs, espresso, sugar, and vanilla together until smooth. Whisk in melted chocolate mixture until smooth. Slowly fold in flour and salt until batter is just combined.
Scrape batter into prepared pan and bake brownies at 350F 18-20 minutes or until a toothpick comes out with moist crumbs sticking to it. Cool brownies completely on a wire cooling rack then chill in fridge several hours until cold.
Using the parchment paper overhang, gently lift brownies out of pan to a cutting board. Cut brownies in half widthwise so you have two 9x6.5 inch long rectangles. Place one brownie rectangle on a parchment paper-lined sheet pan.
Remove ice cream from freezer and scoop onto prepared brownie rectangle and gently spread ice cream into an even layer. Top with remaining brownie rectangle and gently press onto ice cream layer.
Cover pan with plastic wrap and let freeze 4-6 hours* until firm. Use a sharp knife to firmly cut into 6-9 rectangles. Serve ice cream sandwiches immediately or wrap each individual sandwich in plastic wrap and return to freezer. Enjoy!