Adjust the oven rack to the lower third of the oven and preheat to 350°F. Spray the bottom only of a 9-inch round springform pan with non-stick baking spray. Set aside.

Set up a double boiler: fill a saucepan with 2-3 inches of water and place a heat-safe bowl over it — the bowl should not touch the water. Over medium-low heat, melt the butter and chopped chocolate together, stirring often until completely smooth and shiny. Add the sifted cocoa powder and espresso powder and whisk to combine. Remove from heat and set aside to cool slightly.

Separate the eggs, adding the yolks to a medium bowl with the vanilla extract. Whisk together and set aside. Add the egg whites to the bowl of a stand mixer fitted with the whisk attachment. Ensure the bowl is completely clean and grease-free.

Add the cream of tartar to the egg whites. Whip on medium-low until bubbles form, then slowly increase speed to medium-high until soft peaks form. With the mixer running on medium-high, slowly add the granulated sugar one tablespoon at a time until stiff, glossy peaks form.

Fold about one-third of the whipped egg whites into the yolk mixture to loosen it. Then fold in the melted chocolate-butter mixture until just combined.

Add the remaining whipped egg whites in three additions, folding gently with a large spatula until no streaks of chocolate or white remain. Do not over-mix — this will deflate the egg whites and compromise the texture.

Pour the batter into the prepared springform pan. Use an offset spatula to smooth the top evenly.

Bake for 30-35 minutes, until the top has puffed, cracked, and has a smooth matte finish. Beneath the cracks it should still look moist — this is correct.

Allow the cake to cool in the pan for 20 minutes. Run a knife along the edge to release the sides, then unhinge the springform. The cake will deflate as it cools — this is normal and gives it its signature dense, fudgy center.