Preheat oven to 350 degrees. Butter a 13x9x2-inch metal baking pan.
Place butter and unsweetened chocolate in a heavy bottom saucepan and heat over low heat. Stir constantly until melted and smooth. Remove from heat and cool slightly.
In a large bowl, whisk together eggs and sugar until pale yellow, about 3 minutes. Gradually whisk in chocolate mixture. Stir in flour just until combined. Add vanilla extract and chocolate chips. Pour into pan.
Bake for about 25 minutes. Cool completely before frosting.
For frosting, beat butter using an electric mixer until creamy. Gradually add powdered sugar, creme de menthe, and half and half. Beat until smooth. Stir in chocolate chips. Spread frosting on cooled brownies.