For the brownie layer: Grease the sides and bottom of an 8-inch square baking pan and line with 2 pieces of parchment to overhang the edges. Preheat the oven to 350 degrees F.
Combine the butter and mint in a medium saucepan and melt the butter over low heat. Remove from the heat and let sit 10 minutes to infuse. Remove and discard the mint. Rewarm the butter over low heat. Remove from the heat, then add the chocolate and let sit until almost melted; stir until smooth. Whisk in the eggs until smooth. Whisk in the cocoa, flour and salt until smooth. Whisk in the schnapps. Pour into the prepared baking pan and bake until the center is just set (a tester will not come out completely clean), 28 to 30 minutes. Let cool completely.
For the mint layer: Beat the butter in a mixer fitted with the paddle attachment on high speed until light, about 1 minute. Add the confectioners' sugar and salt and mix on low to combine. Add the schnapps and beat on high speed until light and fluffy, about 2 minutes. Add the food coloring, a little at a time, to get a pale green color. Spread the mint layer over the brownies and refrigerate until almost set, about 15 minutes.
For the truffle layer: Melt the butter in a small saucepan over low heat. Stir in the chocolate and remove from the heat; let sit until the chocolate is almost melted, then stir until smooth. Let cool slightly, 5 to 10 minutes, then spread over the mint layer. Top with the sprinkles, if using. Refrigerate until set, about 1 hour. Cut into squares to serve.