Preheat oven to 425°F. Line a half-sheet baking pan with parchment and lightly grease with butter.

In the bowl of a stand mixer fitted with the whisk attachment, combine egg whites, lemon juice, and salt. Beat on medium until foamy. Increase mixer to high and slowly add sugar. Beat until stiff but moist peaks form. Transfer to a bowl and set aside.

In the mixer bowl (no need to clean), combine egg yolks and maple syrup. Whisk on high until pale and thick. Sift flour and cornstarch over the yolk mixture and gently fold in.

Add one-third of the whipped egg whites and gently stir in. Add remaining egg-whites and fold in gently until no streaks remain.

Pour batter into prepared pan and bake for 10 minutes, or until golden brown. Cool completely.

Place half the Kahlua in a microwave-safe bowl and sprinkle the agar-agar on top. Let stand for 3 minutes. Microwave at 50% power in 10-second intervals, swirling in between until agar-agar is completely dissolved.

In the bowl of a stand mixer, combine egg yolks, remaining Kahlua, and maple syrup. Place over a pan of simmering water, and whisk until thick enough to form ribbons when the whisk is raised. Place bowl on stand mixer fitted with the whisk attachment and beat on high until cool, about 5 minutes. Transfer to a large clean bowl and refrigerate.

In the mixer bowl (no need to clean), combine mascarpone and whipping cream and whip on high until stiff peaks form, about 2 minutes.

Remove the egg yolk mixture from the refrigerator and stir a tablespoon into the Kahlua with dissolved agar-agar. Stir until uniform, then pour back into the egg yolk mixture and stir in.

Fold the cream-mascarpone mixture into the egg yolk mixture in three additions.

Run a sharp knife around the edge of the baking sheet to loosen the ladyfingers. Invert and remove parchment. Trim away browned edges. Slice into 3 equal-sized rectangles.

Place one rectangle on a serving plate and brush top with Kahlua. Spread one-third of the filling mixture on top, then dust with cocoa powder until covered. Place a second ladyfinger rectangle on top, brush with Kahlua, then freeze 15 minutes to firm.

Coat with another third of filling mixture, dust with cocoa powder until covered, and place the remaining ladyfinger layer on top. Brush with remaining Kahlua and freeze for 15 minutes to firm.

Top with remaining filling and dust with remaining cocoa.