Heat oven to 350°F. Grease 8-inch square baking pan; set aside.
Combine 1 tablespoon espresso powder and hot water in bowl; stir to dissolve. Set aside.
Melt 1 cup chocolate chips and 1/2 cup butter in 3-quart saucepan over low heat, stirring occasionally, 4-7 minutes or until smooth. Remove from heat; stir in espresso mixture, sugar and vanilla. Add 1 egg at a time, mixing well after each addition. Add flour, baking powder and salt; stir until well mixed.
Spread mixture into prepared pan. Bake 33-38 minutes or until brownies just begin to pull away from sides of pan. (Do not overbake.) Cool completely.
Combine 1 teaspoon espresso powder and 2 tablespoons milk in bowl; stir to dissolve. Add powdered sugar and 1/4 cup butter. Beat at low speed, scraping bowl often and adding enough milk for desired spreading consistency. Frost cooled brownies.
Melt 1/3 cup chocolate chips and shortening in 1-quart saucepan over low heat, stirring occasionally, until smooth.
Drizzle chocolate over frosting; swirl with toothpick or knife for marbled effect.