Melt the chocolate and butter together over low heat, stirring frequently. Remove from heat to cool slightly.
In the bowl of a stand mixer, combine chocolate-butter mixture with sugar, vanilla, and eggs on medium speed for 1 minute, scraping down the sides of the bowl frequently. Mix in flour and salt and beat for 30 seconds. Scrape bowl and beat for 1 minute. Stir in chocolate chips.
Beat the cream cheese until smooth with electric mixer. Scrape sides of bowl and beat in sugar, eggs, and creme de menthe until smooth and fully blended. Add 2 drops food coloring to heighten filling color.
Spread half of brownie mixture in a greased 13 by 9 by 2-inch pan. Pour mint filling on top of brownie batter and spread to edge. Carefully spread the other half of the brownie mixture on top of the mint filling. Bake for 40 to 45 minutes until sides pull away from pan and a toothpick inserted in the center comes out clean. Cool in pan.
Beat butter until smooth with electric mixer. Add sugar and melted chocolate to butter and beat. Slowly add mint extract and enough milk, 1 tablespoon at a time, to make desired consistency. Spread frosting on top of cooled chocolate mint brownies. Sprinkle the crushed candy canes on top of frosting. Cut the bars into 8 rows by 6 rows and serve.