For the Brownies
Preheat the oven to 350°F. Lightly grease a 9" x 13" pan

In a saucepan set over low heat, melt the butter, then add the sugar and stir to combine. Return the mixture to the heat briefly, just until it's hot, but not bubbling; it'll become shiny looking as you stir it. Heating this mixture a second time will dissolve more of the sugar, which will yield a shiny top crust on your brownies.

Transfer the sugar mixture to a medium-sized mixing bowl, if you've heated it in a saucepan. Stir in the cocoa, salt, baking powder, espresso powder, and vanilla.

Whisk in the eggs, stirring until smooth.

Add the flour and chips, again stirring until smooth.

Spoon the batter into a lightly greased 9" x 13" pan.

Bake the brownies for about 30 minutes, until a cake tester inserted into the center comes out clean, or with just a few moist crumbs clinging to it. The brownies should feel set on the edges, and the center should look very moist, but not uncooked.

Remove them from the oven and cool completely on a rack.

For the Frosting
In a bowl cream butter and vanilla. Add powdered sugar and beat on medium speed. Dissolve instant coffee in milk and add to the mixture. Beat until lightly and fluffy.

Spread the frosting over the cooled brownies.