Preheat the oven to 350°F (180°C), then place a rack in the center of the oven. Line the bottom of a 6-inch** springform pan with parchment paper. Do not butter the pan and parchment, just line the bottom. Place pan into a baking tray.
Using the double boiler method, melt the chocolate until smooth. Remove bowl from heat and add in the butter, whisking until fully mixed and smooth. In a small bowl or glass, whisk together coffee liqueur and instant coffee.
In a large bowl, whisk the egg, egg yolks, and half the sugar just until combined. Slowly pour in the warm chocolate mixture, whisking constantly until well-combined. Whisk in the Kahlua-coffee mixture until well-combined.
In a separate medium bowl, use a handheld mixer to beat the egg whites until foamy, about 2 minutes. Gradually add the remaining sugar and beat until glossy medium peaks form, about 5 more minutes. When the beater is lifted, the egg whites should be able to hold their shapes but the tips will curl back and not stand stiff.
Very gently fold about a quarter of the beaten egg whites into the chocolate mixture to lighten it, then gently fold in the remaining egg whites. Mix until everything is combined but do not deflate the mixture.
Scrape the batter into the prepared pan, then smooth the top as necessary. Bake until the top is puffed and cracked and the center is no longer wobbly, 20 to 25 minutes. Be careful not to over-bake this cake! Allow the cake to cool completely in the pan on a wire rack. The center of the cake will sink as it cools, forming a crater. Once cooled, run a thin knife around the cake gently, then unmold.