Preheat the oven to 350°F (175°C). In a saucepan, melt the butter over medium heat until it turns golden brown and has a nutty aroma. Remove from heat and let cool slightly. In a mixing bowl, combine the brown butter, sugar, flour, and salt. Mix until well combined. Press the mixture into the bottom of a greased 9x13 inch baking dish. Bake for 20 minutes or until lightly golden.

Prepare the Lemon Filling

In a mixing bowl, whisk together the eggs, sugar, lemon juice, and lemon zest until smooth. Pour the lemon filling over the baked crust and return to the oven. Bake for an additional 20 minutes, or until the filling is set.

Make the Meringue

While the lemon filling is baking, prepare the meringue. In a clean bowl, beat the egg whites until soft peaks form. Gradually add the sugar, beating until stiff peaks form. Gently fold in the chopped mint and lime leaves.

Combine and Finish

Once the lemon filling is set, remove it from the oven and spread the meringue over the top, making sure to cover the filling completely. Use a spatula to create peaks in the meringue. Bake for an additional 10-15 minutes, or until the meringue is golden brown. Allow to cool before slicing into squares.