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1
In a 2- to 3-quart pan, combine 1/2 cup butter and the unsweetened chocolate. Stir often over low heat until melted and smooth. Remove from heat and beat in granulated sugar, 3 tablespoons espresso powder, the eggs, and vanilla until well blended. Stir in flour just until incorporated.
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2
Pour batter into a lightly buttered 8- or 9-inch cake pan with removable rim (see notes). Bake in a 350u00b0 regular or convection oven until center springs back when gently pressed, 20 to 25 minutes. Let cool completely in pan on a rack, about 1 hour.
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3
In a bowl, combine remaining 1/4 cup butter and 1 tablespoon espresso powder with the powdered sugar and 2 tablespoons liqueur. With an electric mixer on medium speed, beat mixture until smooth and fluffy, adding up to 1 more tablespoon liqueur if necessary to make a smooth, spreadable mixture. Spread evenly over the top of the cool brownie cake.
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4
Place chocolate chips in a 1-quart unpleated zip-lock plastic bag. Heat in a microwave oven at full power (100%) at 15-second intervals, squeezing chocolate between intervals, until melted and smooth, about 1 1/4 minutes total. Squeeze chocolate to one corner of the bag, then cut off about 1/4 inch of that corner. Pipe chocolate decoratively over buttercream. Chill until chocolate is firm, at least 30 minutes.
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5
Just before serving, remove pan rim. Cut brownie cake into wedges and set on plates.
