Make the cake: Arrange a rack in the center of the oven and heat to 350 degrees. Butter only the bottom, not the sides, of a 9-by-13-by-2-inch baking pan. (The cake will rise higher as it bakes and will have less of a domed top without any butter on the sides of the pan.)

Sift the flour and baking powder into a small bowl and set aside. Whisk the coffee and the cocoa powder in a separate small bowl until smooth and no lumps of cocoa remain. Let sit for 5 minutes to bloom and bring out the rich chocolate flavor. Stir in ½ cup/60 milliliters whole milk and set aside.

Add the eggs, granulated sugar, vanilla and salt to the bowl of an electric mixer fitted with the whisk attachment and beat on high speed until the mixture is thick, pale and foamy and almost tripled in volume, 8 to 10 minutes. Reduce the speed to low and slowly add half the flour mixture, all of the coffee mixture, and finally the remaining flour mixture. Scrape the sides and bottom of the bowl with a rubber spatula to be sure the batter is well mixed and fold any streaks of white into the darker batter until completely uniform. Pour the batter into the prepared pan, smooth the top and bake until a cake tester inserted in the center of the cake comes out clean, 22 to 27 minutes. Let sit in the pan to cool for at least 1 hour.

While the cake cools, whisk together the remaining 1 ¼ cups/335 milliliters whole milk and the chocolate hazelnut spread in a medium bowl until completely smooth and no lumps remain. Add the heavy cream and evaporated milk and stir to combine. Using the tines of a fork, poke holes all over the cooled cake (about ½-inch apart) and slowly pour the milk mixture over the cake, allowing it to soak in and pool over the top. Milk mixture will take about 10 to 30 minutes to fully absorb and your cake may float in the mixture and that is OK. Cover the cake with plastic wrap and refrigerate for at least 6 hours and up to 24.

Make the whipped cream: Add the heavy cream, powdered sugar, vanilla and salt to the bowl of an electric mixer fitted with the whisk attachment. Beat on medium speed until soft peaks form, about 5 minutes. Transfer 1 cup of whipped cream to a medium bowl and stir in the chocolate hazelnut spread until creamy and completely incorporated. The cream may deflate a bit and that's OK. With the mixer on low speed, slowly add the chocolate hazelnut mixture to the whipped cream and continue to beat until completely combined. Scrape the sides and bottom of the bowl with a rubber spatula to be sure the whipped cream is well mixed and fold any streaks of white into the darker cream until completely uniform.

Spread the cream mixture over the top of the cake and chill for at least 30 minutes until the cream is firm. Top with sprinkles and serve cold. Cover and refrigerate any leftovers for up to three days.