Frosting:

Preheat the oven to 350°F. Line a baking sheet with parchment.

Scatter the pecans evenly over the baking sheet and toast in oven for about 5 minutes, until lightly toasted and fragrant. Cool the nuts completely and chop.

In a medium saucepan, combine the milk, cream of coconut, and butter and cook over medium heat, stirring, until the butter is completely melted. Remove from the heat and stir in the vanilla.

In a medium bowl, whisk the egg yolks, sugar, cornstarch, and salt together until smooth. Slowly pour in about ¼ cup of the hot milk mixture to temper the eggs, so they won’t curdle, and then, whisking constantly, add the remainder of the milk in a steady stream. Continue to whisk until the mixture thickens, 10 to 12 minutes. Stir in the coconut and pecans.

Let cool completely before frosting the cake. The frosting can be made ahead and stored in an airtight container in the refrigerator for up to 1 week.

Make the cake

Position a rack in the lower third of the oven and preheat the oven to 350°F (175°C). Butter a 9-by-13-by-2-inch baking pan or coat with nonstick spray. Line the pan with parchment, leaving an overhang on two opposite sides. (I did not use parchment and served this cake directly from the baking dish.)

Put the chocolate in a medium bowl and pour in the hot coffee and vanilla. Let stand for about 2 minutes to melt the chocolate, then whisk until smooth.

While the chocolate is melting, in the bowl of a stand mixer fitted with the paddle attachment (or in a large mixing bowl, using a handheld mixer), combine the flour, sugar, baking soda, and salt. Let the mixer run on low speed for 2 to 3 minutes to aerate the flour.

In a medium bowl, whisk the eggs and oil together until thick, satiny, and light in color. Whisk in the sour cream, being careful not to overmix; leave some visible streaks of white.

Pour in the melted chocolate mixture and mix until just combined.

With the mixer on medium speed, add the chocolate–sour cream mixture to the dry ingredients in thirds, mixing until well blended. Remove the bowl from the mixer stand (if using) and, using a rubber spatula, incorporate any ingredients hiding at the bottom of the bowl, making sure the batter is completely mixed.

Scrape the batter into the prepared pan and smooth the top with a spatula being careful there are no air bubbles.

Bake for 35 to 40 minutes, until a cake tester inserted in the center of the cake comes out clean. Let the cake cool in the pan on a wire rack for about 20 minutes, or until cooled completely.

Frost the top of the cake with frosting.

The cake can be stored, loosely covered, in the refrigerator for up to 3 days. Bring to room temperature before serving.