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To make the cake, preheat the oven to 350 degrees F.
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Dissolve the coffee granules in the boiling water and let cool.
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Lightly grease or spray a 13" x 9" baking dish with nonstick cooking spray and line the bottom with waxed paper.
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In a large bowl, mix together the flour, sugar, cocoa, baking powder, baking soda and salt.
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Whisk the milk with the yogurt until blended and add to the flour mixture along with eggs, oil, vanilla and coffee mixture.
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Beat at medium speed for 2 minutes.
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Pour into the prepared pan.
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Bake for 40 to 45 minutes or until the top springs back when lightly touched.
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Let cool in the pan for 20 minutes.
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Remove from the pan and cool completely on a rack.
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To make the chocolate icing, mix the sugar and cocoa in a small saucepan.
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Whisk in the milk until smooth.
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Over medium heat, bring to a simmer, stirring constantly.
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Continue cooking and stirring for 2 minutes.
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Remove from the heat and stir in the vanilla.
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Let cool for 2 hours (the icing thickens as it cools.).
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Spread over the top of the cake.
