Preheat oven to 350° degrees F. Line a 9x9" light metal square baking pan with foil, extending the sides of the foil over the edges of the pan. Spray the foil with cooking spray; set aside.
In a medium bowl, combine the melted butter and granulated sugar until combined. Whisk in the vanilla extract and eggs, one at a time, mixing well after each addition. Lastly, mix in the cocoa powder, salt, flour, and instant espresso powder if using until a soft batter comes together. Pour the batter evenly into the prepared pan and smooth out the top.
Bake the brownies for 22-25 minutes or until a toothpick inserted near the center comes out clean or with moist, but not wet, crumbs. Cool completely.
For the mousse: In a small saucepan, combine the miniature marshmallows, chopped chocolate bar and 1/4 cup of Bailey's liqueur over low heat. Cook, stirring constantly, until everything is melted and smooth. Remove from heat and cool completely, about 10 minutes.
After chocolate mixture has cooled, whip the heavy whipping cream and remaining 2 Tablespoons of Bailey's liqueur together on high speed until stiff peaks form, about 5-7 minutes. Fold the chocolate mixture into the whipped cream mixture gently until no white streaks remain. Spread the mousse evenly over the brownies in the pan. Cover and refrigerate for at least 2 hours to firm and set.
Just before serving, top the brownies with the ganache. For the ganache: microwave the heavy cream in a microwave-safe bowl or cup for about 30 seconds or until hot. Pour over the chocolate chips in a small bowl and let stand for about 5 minutes or until softened. Whisk until melted and smooth. Pipe or drizzle over the brownies. Cut into squares and serve. Store any leftover brownies in the fridge covered to keep the mousse from drying out.