Spray a 9 by 13-inch baking pan with nonstick spray. Whisk 1/3 cup of water, oil, eggs, and 2 tablespoons espresso powder in a large bowl to blend. Add the brownie mix. Stir until well blended. Stir in the chocolate chips. Transfer the batter to the prepared baking pan. Bake until a toothpick inserted into the center of the brownies comes out with a few moist crumbs attached, about 35 minutes. Cool completely.
Meanwhile, dissolve the remaining 2 teaspoons of espresso powder in the remaining 2 tablespoons of water in a medium bowl. Whisk in the vanilla. Add the powdered sugar and butter and whisk until smooth. Pour the glaze over the brownies. Refrigerate until the glaze is set. Cut into bite-size pieces. Arrange the brownies on a platter and serve.