Preheat oven to 350°F. Butter and flour an 8x8x2-inch baking pan.
In a small saucepan, melt butter over low heat. Remove from heat and add chocolate. Stir until all chocolate is melted and well combined. Set aside to cool down.
In the bowl of a stand mixer using the whisk attachment, beat at high-speed the eggs, brown sugar, vanilla, and salt. Beat for 5 to 6 minutes until mixture thickens and becomes pale in color. Remove bowl from mixer. Add chocolate mixture in 3 stages and fold into the egg mixture. Fold flour gently into egg-chocolate mixture until well incorporated.
Pour batter into prepared pan. Place in oven and bake for 20 minutes. Do not overbake. Remove from oven and cool completely. About 1 hour.
Prepare the frosting. In the bowl of an electric mixer fitted with the paddle attachment, beat the butter at medium speed until fluffy, about 2 minutes. Add the powdered sugar, peppermint extract, and milk and beat at low speed until all ingredients are combined. Increase speed to medium-high and beat for 2 additional minutes. Once the brownies are completely cooled down, evenly spread the frosting over the brownies. Place in the refrigerator for 15 minutes.
Prepare the bark. In a small saucepan, at low heat melt chocolate chips and butter. Stir until the mixture is well combined. Remove brownie from the refrigerator, and spread the chocolate over the frosting. Sprinkle crushed peppermint candy on top. Let chocolate harden before cutting into pieces. Serve.