Preheat oven to 350 degrees (325 degrees for dark-coated metal pan). Position a rack in the lower third of the oven. Spray the bottom only of a 13x9-inch baking pan with nonstick cooking spray (or foil-line pan).
Combine the brownie mix, oil, water, eggs and ½ teaspoon peppermint extract in a medium mixing bowl with a wooden spoon until just blended and all dry ingredients are moistened. Stir in the chocolate chips. Spread batter into prepared pan.
Bake 28-30 minutes or until toothpick inserted 2 inches from side of pan comes out clean or almost clean (do not over bake). Transfer to a wire rack and cool completely.
Prepare mint frosting: Beat the powdered sugar, 1/3 cup softened butter, and ¾ teaspoon peppermint extract in a medium bowl with an electric mixer set on low speed until smooth. Beat in milk, 1 tablespoon at a time, until smooth and spreadable. Beat in green food coloring, if desired.
Spread frosting over cooled brownies.
Prepare chocolate glaze: Melt chocolate chips, 2 tablespoons butter and corn syrup in a small saucepan set over low heat, stirring occasionally, until melted and smooth. Stir in hot water, a few drops at a time, until mixture is thin enough to drizzle.
Drizzle chocolate glaze over frosting.
Refrigerate for 1 hour to set the glaze. Cut into squares. Store in refrigerator.