Preheat the oven to 250°. Make the meringue: In a stand mixer on high speed, beat the egg whites until very stiff peaks form, 2-3 minutes.
Meanwhile, in a food processor, pulse the almond flour, sugar, and cornstarch until the mixture reaches a fine, sandy consistency. Transfer to a large bowl.
Trace out three 10 inch circles on parchment paper as a guide. Set them on 1-2 large baking sheets lined with silicone mats.
Using a rubber spatula and working in three batches, fold the egg whites into the almond mixture until thoroughly combined. Scoop the mixture evenly onto the traced circles and, using an offset spatula, spread the meringue evenly to fill the circles (they will be about 1⁄4 inch high each).
Bake, rotating the pans fully every 10 minutes, until an even golden brown is achieved, about 2 hours and 20 minutes (though time will vary with consistency and humidity).
Remove and let cool slightly. The shells will have a tendency to stick; work slowly and carefully to remove parchment from them (the rounds will be very fragile).
Make the buttercream: In a high-sided saucepan over medium heat, add the coffee and sugar. Set a candy or deep-fat thermometer into the pan and heat until the mixture registers 265°.
Meanwhile, in the clean bowl of a stand mixer, whisk the egg yolks until the volume has tripled and the color has lightened significantly, about 8 minutes.
Once the syrup has reached temperature, remove and slowly pour the mixture into the yolks, whisking on medium-low speed. Continue to run the mixer for 20-30 minutes, letting the mixture cool completely. Once fully cooled, add the butter 1 tablespoon at a time, whisking until fully incorporated after each addition. (Buttercream will thicken noticeably when the butter has been fully incorporated.)
Place one meringue round on a cake platter. Using an offset spatula, spread all of the buttercream evenly over the meringue within ½ inch of the edge. Carefully place the second shell on top, applying very slight pressure, then chill.
Prepare the chantilly: In the clean bowl of the mixer, whisk the heavy cream, confectioners’ sugar, and rum until stiff peaks form.
Using an offset spatula, spread all of the Chantilly evenly over the meringue within ½ inch of the edge as you did the buttercream, then place the final meringue on top, applying very slight pressure. Return the dacquoise to the refrigerator for at least 12 hours or up to one week.
Before serving, dust the surface of the cake lightly with confectioners’ sugar. Slice with a clean, hot knife and garnish slices with a drizzle of hot fudge.