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1
Preheat the oven to 325 degrees F. Line the bottom of two 8-inch-square metal baking pans with parchment paper and lightly butter the paper.
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2
Sift the flour, baking powder, baking soda and salt into a bowl, then whisk to combine.
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3
Melt the butter in a saucepan over medium heat.
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4
Add the cocoa powder and whisk until dissolved, about 1 minute.
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5
Transfer to a bowl and whisk in both sugars until combined.
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6
Add the coffee, buttermilk, egg and vanilla and whisk until smooth.
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7
Whisk in the flour mixture until just combined.
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8
Divide the batter evenly between the prepared pans.
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9
Bake until a toothpick inserted into the center comes out with a few moist crumbs, 15 to 20 minutes.
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10
Cool slightly in the pans, then invert onto a rack to cool completely.
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11
Transfer the cakes to a baking sheet lined with parchment paper, cover with plastic wrap and freeze until firm, about 1 hour.
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12
Remove the ice cream from the freezer to soften, 10 to 20 minutes.
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13
Clean and dry the baking pans, then line each with plastic wrap, leaving a 4-inch overhang on all sides.
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14
Scoop all of the ice cream into one of the pans, packing it to make an even 1-inch-thick layer; smooth with a small offset spatula or the back of a spoon.
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15
Fold the plastic wrap over the ice cream to cover it, then freeze until solid, at least 1 hour.
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16
Put 1 frozen cake in the remaining plastic-lined pan.
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17
Unwrap the ice cream layer and invert it on top of the cake; remove the plastic wrap.
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18
Cover with the remaining cake, pressing gently.
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19
Fold the plastic wrap over the cake to cover it and freeze until firm, about 1 hour.
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20
When ready to serve, unwrap the cake and cut into 9 squares.
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21
Cut each square in half to make 2 rectangles or triangles.
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22
Photograph by Levi Brown
