Meringue is easy to make, but there are a few things you can do to increase your success rate. First of all, it's good to know that cold eggs are easier to separate, but room-temperature whites make for better meringue. So be sure to give your whites a little time on the counter before getting to work. Secondly, make sure to keep all bits of egg yolk out of the whites. Fat is the enemy of meringue. And double-check that all of your tools and bowls are clean and fat-free as well.
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. In a large bowl using an electric mixer, beat the flour, confectioners' sugar, brown sugar and salt on medium speed until well combined. Add the butter and beat until the crumbs are evenly moistened. Tip the crumbs into the prepared pan and pat down to make an even base. Bake the base until deep golden and set, 20 to 25 minutes. Transfer to a rack to cool, about 30 minutes. For the filling: In a large bowl, whisk together the sweetened condensed milk, lime zest and juice, egg yolks and salt. Pour the mixture over the baked cookie base and spread it into an even layer. Bake the filling until just set, 8 to 10 minutes. Transfer to a rack to cool, about 30 minutes, then cover with plastic and refrigerate until firm, at least 4 hours. For the topping: Just before serving, make the topping. In a large bowl (or the bowl of a stand mixer fitted with the whisk attachment), add the egg whites. In a small saucepot fitted with a candy thermometer, heat the sugar and 1/4 cup water over medium-high heat without stirring. 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. 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. Continue to beat the mixture until shiny, stiff peaks form and the mixture is cool, about 6 minutes. Scoop the meringue on top of the filling and use an offset spatula to swirl it around into decorative swoops and spikes. Using a mini (kitchen) blowtorch, toast the topping to an even golden brown. Cut into bars and serve.
Propane gas torches are highly flammable and should be kept away from heat, open flame and prolonged exposure to sunlight. They should be used only in well-ventilated areas. Follow torch manufacturer's instructions for use.