Center a rack in the oven and preheat it to 350 degrees F. Lightly butter a 9-inch square baking pan and line it with parchment paper.
To make the topping: Put the sugar in a medium bowl and pour over the egg whites. Using your fingers or a fork, mix until the sugar is moistened. If there are lumps, ignore them. Toss in the almonds and stir them around until they’re coated with the sugared whites. Set aside while you make the batter.
To make the bars: Working in a large bowl, whisk the sugar, eggs and salt together until the mixture lightens in color and thickens a little, about 2 minutes. Whisk in the vanilla and almond extracts. Switch to a flexible spatula and gently stir in the flour. When the flour is fully incorporated, gradually fold in the melted butter. You’ll have a thick batter with a lovely sheen. Scrape it into the pan and use the spatula to work the batter into the corners. The layer will be very thin.
Give the topping another stir, or a run-through with your fingers, and turn it out onto the batter. Use a spatula or your fingers to spread the almonds evenly over the mixture, making sure to get nuts into the corners too.
Bake for 28 to 32 minutes, or until a tester inserted into the center of the cake comes out clean or with only a few crumbs stuck to it. The meringue topping will be pale golden brown. If you’d like a deeper color on the topping, run it under the broiler until you get the shade of gold you like best.
Transfer the pan to a rack and let rest for 5 minutes, then run a knife around the edges of the cake and unmold it onto the rack. Very gently peel away the parchment and invert the cake onto another rack to cool to room temperature.
Transfer the cake to a cutting board and, using a long, thin knife, slice it into nine 3-inch squares. For smaller portions, cut each square into two triangles. If you’d like, you can dust the bars with confectioners’ sugar just before you serve them.
Storing: Wrapped, the bars will keep at room temperature for 4 to 5 days.
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