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1
Position a rack in the center of the oven and preheat to 350 degrees.
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2
Lightly grease a 13-by-18-inch jelly-roll pan; line with parchment paper, letting it come up the short sides by about 2 inches.
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3
Brush the paper with oil or melted butter and lightly dust with flour.
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4
For the filling, whisk the evaporated milk, 1 cup sugar, 3 egg yolks and the cubed butter in a saucepan over medium heat.
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5
Cook, stirring constantly, until thick and creamy, about 10 minutes.
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6
Remove from the heat; stir in 1 teaspoon vanilla, the coconut and pecans.
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7
Set aside to cool completely, stirring occasionally.
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8
Meanwhile, whisk the flour, baking soda and salt in a medium bowl.
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9
Whisk the cocoa and chocolate in another bowl.
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10
Add the hot coffee to the cocoa mixture, stirring until smooth; stir in the buttermilk and the remaining 2 teaspoons vanilla.
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11
Using a mixer, beat the softened butter and the remaining 1 1/4 cups sugar in a large bowl on high speed until fluffy, about 4 minutes.
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12
Reduce the speed to low; add the 3 whole eggs, 1 at a time, incorporating each before adding the next.
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13
Add the flour mixture in 3 parts, alternating with the cocoa mixture in 2 parts, beginning and ending with the flour.
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14
Beat until just blended; if necessary, fold the batter together with a rubber spatula.
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15
Spread the batter evenly in the prepared pan.
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16
Bake until the cake springs back when pressed lightly, about 16 minutes.
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17
Cool slightly in the pan.
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18
Run a knife around the edge and slide the cake with its paper onto a work surface.
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19
Spread the coconut filling evenly over the cake.
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20
Roll the cake from one of the short ends, pulling it away from the parchment into a tight cylinder; transfer to a platter.
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21
Cool completely and dust with the confectioners' sugar or cocoa.
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22
Photograph by Ellie Miller
