TO MAKE THE COFFEE CRUNCH:

Lightly oil a baking sheet.

Combine the sugar, coffee, and corn syrup in a heavy-bottomed, 4-quart saucepan (the mixture becomes very foamy after the baking soda is added and rises high in the pan) and bring to a boil. Cook almost to the hard-crack stage (285°F on a candy thermometer), approximately 6 to 7 minutes. The mixture will be slightly smoky with a strong aroma of coffee as it cooks.

Remove the pan from the heat and count to 10. Sprinkle on the baking soda, making sure to distribute it as evenly as possible, so there are no clumps visible. Whisk just enough to distribute the soda throughout. Be careful, the mixture is very hot and will foam up high, looking like golden lava as it bubbles up. When it stops rising and foaming (after a minute or two) immediately pour it onto the baking sheet. Spread it out with a spatula, and let sit until it has cooled and hardened.

Using a small hammer, break the coffee crunch into irregular ¼- to ½- inch-pieces, you don’t want crumbs. If you do get some, save them for the in-between layer. Store in an airtight container until ready to use. (You can make the coffee crunch up to two days ahead of time. If the weather is humid, the brickle will become moist, don’t worry, just break up the clumps.)

TO MAKE THE CAKE:

Preheat oven to 350°F.

Using an electric mixer, beat the egg whites in a large mixing bowl until they begin to foam. Slowly add 3/4 cups of the sugar, and continue beating until the whites are stiff but still moist. Transfer to a bowl and set aside.

Sift together the flour, the remaining ¾ cup sugar, the baking powder, and the salt in a small mixing bowl. Place the oil, egg yolks, ¾ cup water, lemon zest, and vanilla in a large bowl and beat with an electric mixer until completely smooth. Add the flour mixture and stir to combine well.

Gently fold one third of the beaten whites into the batter. Once incorporated, drop the remaining whites onto the batter and fold them in. Pour the batter into an ungreased 10-inch tube pan, and smooth the top with a rubber spatula.

Bake in the top half of the oven for 80 to 90 minutes, or until a wooden skewer inserted in the cake comes out clean. Remove from the oven and immediately invert the pan onto the neck of a wine bottle until it is completely cool. Turn the pan right side up and use a knife to go around the side of the pan to loosen the cake, push the center up and remove the cake from the pan. When done, wrap in plastic wrap until ready to frost—it will keep for a day.

TO MAKE THE FROSTING:

Combine the cream and vanilla in a deep bowl. Sift the confectioners’ sugar and instant coffee together twice, then add to the cream and vanilla. Using a whisk, rotary, or electric beater, whip the cream until soft peaks form. It must be stiff enough to spread.

TO ASSEMBLE:

Split the cake into 2 equal layers. Using a spatula, frost the bottom layer and sprinkle it with the coffee crunch. Place the second cake layer on top, frost it, and sprinkle the top and the side of the cake generously with the coffee crunch.