Preheat your oven to 350°F (175°C). Line a 9x13-inch baking pan with parchment paper, leaving some overhang on the sides.
In a medium mixing bowl, whisk together the flour, salt, and cocoa powder. In a double boiler or microwave-safe bowl, melt the coarsely chopped dark chocolate and butter together until smooth. Stir in the sugars until well combined.
Once the chocolate mixture has cooled slightly, whisk in the eggs, one at a time, followed by the vanilla extract. Mix until the batter is shiny and smooth.
Gradually add the flour mixture to the chocolate mixture, stirring until just combined. Do not overmix. Pour the brownie batter into the prepared baking pan, spreading it out evenly.
Bake in the preheated oven for about 20-25 minutes or until a toothpick inserted into the center comes out with a few moist crumbs. Let the brownies cool completely in the pan on a wire rack.
In a mixing bowl, combine the sugar, flour, milk, and heavy cream. Mix until smooth. In another bowl, beat the softened butter, creme de menthe, and peppermint extract together until creamy. Gradually add the milk mixture to the butter, beating until well combined.
Once the brownies are completely cool, spread the mint filling evenly over the top. Smooth it out with a rubber spatula.
In a double boiler or microwave-safe bowl, melt the dark chocolate along with the light corn syrup and butter until smooth. Stir until fully combined and glossy.
Pour the chocolate topping over the mint layer, spreading it out evenly. Allow the bars to set in the refrigerator for at least 2 hours.
Once set, lift the bars out of the pan using the parchment paper overhang. Slice into squares or bars and serve chilled or at room temperature.