Bring 1 1/2 cups water to a boil, and remove from heat. Add coffee; cover and let stand for 10 minutes. Strain through a cheesecloth-lined sieve into a medium bowl; discard solids. Cover and refrigerate until needed.
Combine 1/4 cup sugar, egg yolks, and 1 tablespoon Kahlúa in the top of a double boiler, stirring well with a whisk. Cook over simmering water, whisking constantly, until thick and candy thermometer registers 160° (about 9 minutes). Remove from heat; refrigerate 10 minutes.
Place egg whites in a large bowl; beat with a mixer at high speed until medium peaks form. Combine the remaining 1/4 cup sugar and 2 tablespoons water in a small saucepan, and bring to a boil. Cook, without stirring, until the candy thermometer registers 250°. With mixer on low speed, carefully pour hot syrup over egg whites. Gradually increase speed to high; beat for 2 minutes or until stiff peaks form (do not overmix).
Combine egg yolk mixture, cream cheese, and mascarpone cheese in a large bowl, and beat with a mixer at medium speed until smooth. Gently stir one-fourth of egg white mixture into cream cheese mixture; gently fold remaining egg white mixture into cream cheese mixture.
Add remaining 1 tablespoon Kahlúa to coffee. Quickly dip 12 ladyfingers into coffee mixture; arrange in the bottom of an 11 x 7inch baking dish. Spread half of cream cheese mixture over ladyfingers. Sprinkle with half of chocolate. Repeat procedure with the remaining ladyfingers, coffee mixture, and cream cheese mixture. Sprinkle with remaining chocolate. Cover and chill at least 2 hours.
We like our coffee überstrong here--you can also substitute 1 1/2 cups strong brewed coffee mixed with a tablespoon of instant espresso.