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For the cake: Preheat the oven to 350 degrees F. Lightly grease four 4-ounce "bake and give" paper loaf pans.
Place the almond paste in the bowl of an electric stand mixer fitted with the paddle attachment. Mix until the paste has softened and broken down into small pieces. Slowly incorporate the eggs, one at a time, scraping down the bowl after each addition. Add the cornstarch and salt and mix just until incorporated, then add the melted butter and liqueur and mix just until incorporated (otherwise the batter might break).
Transfer the batter to the prepared pans. Bake until golden brown and a toothpick inserted in the center of the cakes comes out clean, about 25 minutes.
Set the cakes aside to cool.
For the icing: In the bowl of the stand mixer fitted with the paddle attachment, combine the sugar, cream, liqueur and lime juice until the mixture is viscous enough to spread, adding more sugar if necessary.
Cover the surface of the icing with plastic wrap and let it rest overnight in the refrigerator.
To assemble: Stir the lime zest into the icing and ice the cakes immediately with a small offset spatula. Let the cakes sit at room temperature until the icing has set completely and does not stick when touched, about 20 minutes.