Preheat oven to 350°F (175°C).
Combine espresso powder and hot water in small bowl; stir to dissolve. Set aside.
Melt chocolate chips and butter in 3-quart saucepan over low heat, stirring occasionally, until smooth (4 to 7 minutes). Remove from heat; stir in espresso mixture, sugar and vanilla. Add eggs, one at a time, mixing well after each addition. Add flour, baking powder and salt; stir until well mixed.
Spread mixture into greased 8-inch square baking pan. Bake for 33 to 38 minutes or until brownies just begin to pull away from sides of pan. (DO NOT OVERBAKE) Cool completely.
For Frosting: Combine espresso powder and milk in small bowl; stir to dissolve. Add powdered sugar and butter. Beat at low speed, scraping bowl often and adding enough milk for desired spreading consistency. Frost cooled brownies.