Coffee-Caramel Swiss Roll

Preheat oven to 350 degrees. Brush a 13-by- 18-inch rimmed baking sheet with oil. Line bottom with parchment; brush parchment with oil.

Cake:

Whisk together flour, salt, and baking powder to combine. In a large heatproof bowl, whisk hot water with 1/2 cup granulated sugar until dissolved. Whisk in oil, then egg yolks and vanilla until smooth. Whisk flour mixture into sugar mixture just until combined. In a mixer fitted with the whisk attachment, beat egg whites on medium-low speed until frothy. Add cream of tartar, increase speed to medium-high, and continue beating until soft peaks form. Gradually add remaining 1/4 cup granulated sugar; continue beating until stiff, glossy peaks form. Stir one-third of egg whites into batter. Gently fold in remaining egg whites just until no white streaks remain. Transfer to sheet; spread evenly to edges with an offset spatula.

Bake until pale golden and pulling away from edges, and top springs back when lightly touched, 17 to 19 minutes. Let cool on a wire rack 5 minutes. Meanwhile, generously dust a kitchen towel with confectioners' sugar. Flip cake out onto towel, remove parchment, and generously dust top with more confectioners' sugar. Starting at one short end, roll up cake in towel. Let cool completely, about 1 hour.

Syrup:

Meanwhile, in a small saucepan, bring granulated sugar and 3 tablespoons water to a boil, stirring until dissolved. Remove from heat; whisk in espresso powder until dissolved (mixture will foam). Transfer to a heatproof bowl and refrigerate until cold, about 30 minutes.

Filling:

Meanwhile, prepare an ice-water bath. In a saucepan, combine granulated sugar, 1 tablespoon water, and salt. Cover; cook over medium heat, swirling a few times, until boiling and sugar has dissolved, about 5 minutes. Uncover and continue boiling, undisturbed, until mixture turns golden amber, 3 to 5 minutes more. Remove from heat. Carefully add cream in a slow, steady stream (it will bubble up and splatter). Return to medium heat; cook, stirring, until smooth. Transfer to a bowl set in ice-water bath; let stand, stirring a few times, until cold, about 30 minutes. Remove from bath; whisk to stiff peaks.

Unroll cake. Brush any residual sugar from top, then brush evenly with espresso syrup. Dollop with filling and spread evenly with an offset spatula, leaving a 1/2-inch border. Starting at one short end, roll up cake (without towel). Wrap cake roll in towel and transfer to a baking sheet, seam-side down, to maintain cylindrical shape. Refrigerate until filling sets, at least 8 hours and up to 1 day.

Frosting:

In a saucepan, bring 2 inches of water to a simmer over medium heat. In a large heatproof bowl, combine egg whites, granulated sugar, cream of tartar, corn syrup, and water. Transfer bowl to pan (do not let bottom touch water). Beat on high speed until stiff peaks form, about 5 minutes. Remove bowl from heat; continue beating on high until mixture is no longer warm to the touch, about 5 minutes more.

Remove cake roll from towel; transfer to a cake plate. Spread frosting evenly over top and sides. (Frosted cake can be refrigerated, uncovered, up to 3 hours before slicing and serving.) Briefly wave a kitchen torch over frosting until golden brown in places. Slice cake into rounds; serve.