Preheat oven to 350°F (177°C). Grease a 12×17-inch baking pan with nonstick spray or butter, then line it with parchment paper.
Using a fine mesh sieve, sift the cake flour, cocoa powder, baking powder, and salt together. Set aside.
Using a hand mixer or a stand mixer fitted with whisk attachment, beat the egg whites and ¼ cup (50g) granulated sugar together on high speed for 4–5 minutes or until foamy-looking medium peaks form.
In the same mixing bowl, add the egg yolks and remaining sugar. Mix on high speed for 1 minute, then add the oil, milk, vanilla, and espresso powder. Beat together on high speed for 2 minutes.
Add half of the whipped egg whites into the egg yolk mixture. Mix on low speed for 10 seconds. Repeat with remaining egg whites and mix on low for 10 seconds.
Sift in the flour mixture, and then fold the batter together with a silicone spatula until combined.
Spread batter evenly into prepared pan. Bake for 12–14 minutes or until the top of the cake lightly springs back when touched.
Dust parchment/towel with about 2 Tablespoons of cocoa powder. Once the cake comes out of the oven, quickly run a knife around the edges to loosen it from the pan. Immediately invert it onto the parchment/towel.
Starting with the narrow end, begin tightly rolling the hot cake up with the parchment/towel. Allow the cake to cool completely at room temperature rolled up in the parchment/towel, about 3 hours.
Using a hand mixer or a stand mixer fitted with a whisk attachment, whip the heavy cream, sugar, and vanilla extract on medium-high speed until medium to stiff peaks form.
Slowly and gently unroll the cake. Spread whipped cream evenly on top, leaving about a ½-inch border around the cake. Gently roll the cake back up.
Place on a wire rack set on a baking sheet. Set aside as you prepare the ganache.
Place chopped chocolate and corn syrup in a medium bowl. Heat the cream in a small saucepan until it begins to gently simmer. Pour over chocolate, then let sit for 2–3 minutes to gently soften the chocolate. Slowly stir until completely combined.
Pour ganache all over cake roll. Refrigerate for at least 30–60 minutes before slicing and serving.
