Step 1

Crack 5 large eggs into the bowl of a stand mixer (or large bowl if using an electric hand mixer). Let sit until room-temperature, about 45 minutes.

Step 2

Meanwhile, arrange a rack in the middle of the oven and heat the oven to 400°F. Coat a 15x18-inch rimmed baking sheet with cooking spray. Line the bottom of the baking sheet with parchment paper and coat the parchment with cooking spray. Dust with cocoa powder, tapping out any excess. Place 3 tablespoons very hot tap water and 1 tablespoon espresso powder in a small bowl and whisk until combined and smooth.

Step 3

Beat the eggs with the whisk attachment on medium-high speed until lightened in color and foamy, 2 to 3 minutes. Gradually add in 3/4 cup packed light brown sugar and beat until the eggs have tripled in volume and the batter forms ribbons when the whisk is lifted, 4 to 5 minutes more.

Step 4

Add the espresso mixture and 2 teaspoons vanilla extract and beat on medium-low speed until combined. Stop the mixer. Sift 1/2 cup cake flour, 5 tablespoons Dutch process cocoa powder, 1 teaspoon baking powder, and 1/2 teaspoon kosher salt into the bowl. Gently fold together by hand with a flexible spatula.

Step 5

Pour the batter onto the baking sheet and nudge it into the corners with your spatula. Bake until a skewer inserted in the center comes out clean and the cake just begins to pull away from the sides of the pan, 5 to 7 minutes. Meanwhile, place a clean kitchen towel on the counter and sift cocoa powder over it.

Step 6

Remove the cake from the oven. Immediately sift cocoa powder over the top of the warm cake. Run a butter knife around the edges of the pan to release the cake. Invert the cake onto the cocoa-dusted dish towel and carefully remove the parchment paper. Sift more cocoa powder over the cake. Starting at a short end, gently roll up the cake along with the dish towel. Place the rolled-up cake seam-side down on a wire rack and let cool until room temperature, at least 30 minutes. Meanwhile, remove 3 cups ice cream from the freezer and place on the counter to soften for about 20 minutes before you are ready to assemble the roll.

Step 7

Carefully unroll the cooled cake. Using an offset spatula or butter knife, spread the ice cream onto the cake in an even layer, leaving a 1/2-inch border. Gently re-roll the cake without the towel. Arrange seam-side down. Tightly wrap the roll in plastic wrap, manipulating the cake a bit once wrapped to tighten up the roll and push together any cracks. Freeze until the ice cream hardens, at least 4 hours or up to 1 week. About 20 minutes before serving, make the magic shell.

Step 8

Place 1 1/2 cups semisweet chocolate chips and 3 tablespoons oil or shortening in a medium microwave-safe bowl. Microwave on HIGH in 30-second bursts, stirring between each burst, until the chocolate is fully melted, 1 to 1 1/2 minutes total. Let the mixture cool until barely warm, about 20 minutes.

Step 9

Unwrap the roll and place on a serving platter. Immediately pour the chocolate mixture over it. Let sit for a minute for the shell to harden before slicing crosswise and serving. The ice cream roll is best enjoyed immediately, as the magic shell will crack if frozen and then sliced.