Step 1

Heat the oven to 350°F with a rack in the middle position. Butter an 8-inch square pan, line the bottom with a parchment square and butter the parchment.

Step 2

In a medium saucepan over medium, melt the butter. Remove from the heat and add the chocolate, cocoa and espresso powder. Let stand for a few minutes to allow the chocolate to soften, then whisk until the mixture is smooth; cool until barely warm to the touch.

Step 3

In a large bowl, vigorously whisk the egg yolks and 107 grams (½ cup) of the sugar until lightened and creamy, about 30 seconds. Add the chocolate mixture and whisk until homogeneous. Add the almond flour and salt, then whisk until fully incorporated. Whisk in the rum; set aside.

Step 4

In a stand mixer with the whisk attachment or in a large bowl with a hand mixer, whip the egg whites on medium-high until frothy, 1 to 2 minutes. With the mixer running, gradually add the remaining 53 grams (¼ cup) sugar, then beat until the whites hold soft peaks, about 2 minutes. Add about a third of the whipped whites to the yolk-chocolate mixture and fold with a silicone spatula to lighten and loosen the base. Scrape in the remaining whites and gently fold them into the batter until no streaks remain. Transfer to the prepared pan and gently shake or tilt the pan to level the batter.

Step 5

Bake until the cake is slightly domed and a toothpick inserted at the center comes out with a few crumbs attached, 30 to 35 minutes. Cool in the pan on a wire rack for 30 to 45 minutes; the cake will deflate slightly as it cools.

Step 6

Run a paring knife around the inside edge of the pan to loosen the cake, then invert onto a platter; if needed, peel off and discard the parchment. Cool completely. Dust with cocoa before serving.