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Preheat oven to 325 degrees
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Prepare a large 9x13 glass baking dish by spraying it with cooking spray
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Stir together the brownie mix, water, oil and egg in a large bowl and pour in the pan. Bake for 30 minutes or until the brownies no longer jiggle and an inserted toothpick comes out fairly clean.
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Allow to cool for 15 minutes and then poke holes in the top of the brownies and brush 2 TBLS of Kahlua over the top. Place in the refrigerator for 30 minutes to continue cooling.
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In the meantime make the frosting by placing the cocoa in a large mixing bowl and pour the boiling water over it. Stir with a spoon until well combined.
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Add the butter and blend it until well mixed. Add the 3 remaining TBLS of Kahlua and mix until combined.
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Add the powdered sugar and mix until smooth and creamy. Taste it. If you want more Kahlua flavor, add another TBLS. Add a little more powdered sugar if necessary until desired consistency is reached.
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Remove the brownies from the refrigerator and scoop the ice cream over the top and smooth it into a flat layer. Place covered in the freezer for ten minutes.
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Remove and spread the frosting over the top. Cover and place in the freezer for at least an hour before serving. Store any remaining dessert covered in the freezer.