Let sit the vanilla ice cream at room temperature 5 minutes to soften. Line a 9x13 inch baking dish with parchment paper. Spread the ice cream out in an even layer in the prepared pan, freeze 1 hour, until firm.
Make the brownies:
Preheat the oven to 350 degrees F. Line a 9 1/2 x 14 1/2 inch jelly roll pan with parchment paper.
In the microwave, melt together the salted butter and chocolate chips until melted and smooth. Stir in the sugar, vanilla, and instant coffee.
In a small bowl whisk the eggs for 1 minute until bubbly on top. Stir the eggs into the chocolate mix. Add the flour, cocoa powder, and baking powder. Stir until just combined.
Spread the batter into the prepared baking pan. Bake for 20-25 minutes or until the brownies are just set. Remove the brownies from the oven and let them cool completely.
Remove the vanilla ice cream slab from the freezer and invert it onto the center of the brownies. Trim the edges off the brownie around the ice cream, reserving the scraps for later. Place the pan in the freezer to harden for at least 30 minutes.
Remove the brownies and the vanilla ice cream from the freezer and spread the peanut butter over the vanilla ice cream. If desired, top with the reserved brownie crumbs. Freeze until firm, 1-2 hours.
Remove from the freezer and, working quickly, cut into 8-10 square bars. Insert a popsicle stick into one end of each bar. Return to the freezer until frozen solid, at least 2 hours, or overnight.
Make topping by melting chocolate and unsalted butter together in the microwave until melted and smooth. Let cool 2-3 minutes. Remove the bars from the freezers and cover in chocolate. Keep in the freezer until ready to serve.