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1
Heat oven to 350 degrees F.
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2
Stand cones on an ungreased baking sheet.
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3
In a mixing bowl, whisk together the flour, baking soda, and salt; set dry ingredients aside.
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4
Set a medium saucepan full of water over medium heat; bring water to a boil.
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5
Reduce heat to medium high, and let water simmer.
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6
In the heatproof bowl of an electric mixer, combine brewed coffee, 2 1/2 ounces chocolate, and 1/2 cup (1 stick) butter.
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7
Set bowl over simmering water, stirring occasionally, until the butter and chocolate have melted.
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8
Remove bowl from heat; stir in 1 cup sugar.
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9
Transfer bowl to mixer.
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10
Add the reserved dry ingredients, and beat until well combined.
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11
Add the egg and 1 teaspoon vanilla; beat to combine.
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12
Pour batter into the cones, filling each cone 3/4 full.
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13
Transfer baking sheet to oven, and bake until domes form and a cake tester inserted into centers come out clean, 20 to 25 minutes.
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14
Remove from oven, and transfer to a wire rack to cool completely.
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15
Combine the remaining 1/2 cup plus 2 tablespoons sugar, espresso, and cream in a heavy saucepan.
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16
Set over high heat, and bring to a boil, stirring constantly.
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17
Reduce heat to medium; simmer, without stirring, 5 minutes.
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18
Remove pan from heat; add remaining 2 1/2 ounces chocolate, stirring until melted.
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19
Stir in the remaining 1/4 cup (1/2 stick) butter and 1/2 teaspoon vanilla.
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20
Chill, stirring occasionally, until icing is cool enough to spread.
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21
Using an offset spatula, spread icing over ice-cream-cone tops.
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22
Serve.
