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Special equipment: a candy thermometer; a kitchen blowtorch
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For the cookie base.
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Preheat the oven to 350 degrees F. Butter a 9-inch square baking pan and line with parchment paper, leaving a 2-inch overhang on 2 sides.
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In a large bowl using an electric mixer, beat the flour, confectioners' sugar, brown sugar and salt on medium speed until well combined.
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Add the butter and beat until the crumbs are evenly moistened.
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Tip the crumbs into the prepared pan and pat down to make an even base.
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Bake the base until deep golden and set, 20 to 25 minutes.
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Transfer to a rack to cool, about 30 minutes.
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For the filling: In a large bowl, whisk together the sweetened condensed milk, lime zest and juice, egg yolks and salt.
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Pour the mixture over the baked cookie base and spread it into an even layer.
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Bake the filling until just set, 8 to 10 minutes.
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Transfer to a rack to cool, about 30 minutes, then cover with plastic and refrigerate until firm, at least 4 hours.
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For the topping: Just before serving, make the topping.
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In a large bowl (or the bowl of a stand mixer fitted with the whisk attachment), add the egg whites.
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In a small saucepot fitted with a candy thermometer, heat the sugar and 1/4 cup water over medium-high heat without stirring.
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When the thermometer hits about 220 degrees F, beat the egg whites with an electric mixer on medium speed until just frothy and the yellowish hue has disappeared.
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When the sugar reaches 238 degrees F, increase the mixer speed to high and, with the mixer running, pour the sugar syrup into the bowl in a thin stream.
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Continue to beat the mixture until shiny, stiff peaks form and the mixture is cool, about 6 minutes.
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Scoop the meringue on top of the filling and use an offset spatula to swirl it around into decorative swoops and spikes.
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Using a mini (kitchen) blowtorch, toast the topping to an even golden brown.
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Cut into bars and serve.
