Make the Crust: Preheat oven to 350 degrees F. Lightly butter an 8x8-inch square baking pan, then line it with parchment paper, leaving an overhang on each side. Set aside.
Using an electric mixer, beat together the butter and brown sugar on medium speed until light and fluffy, about 3 minutes. Add the egg and mix to combine. Scrape down the sides of the bowl, reduce the mixer speed to low, and add the flour and graham cracker crumbs, mixing until a dough forms. Transfer the dough to the prepared pan and pat into an even layer (the dough will be rather soft). Bake for 10 to 15 minutes, or until light golden brown. Remove from the oven and place on a wire cooling rack.
Make the Filling: Using an electric mixer with a whisk attachment, beat the yolks on high speed until pale and fluffy, 2 to 3 minutes. Gradually add the condensed milk and beat until light and fluffy, an additional 3 to 5 minutes. Scrape down the sides of the bowl, add the lemon juice and beat on medium speed until combined, about 30 seconds to 1 minute.
Pour the filling over the crust and bake for 15 to 20 minutes, or until the filling is set and the center does not jiggle when the pan is moved. Remove from the oven and place the pan on a wire rack to cool to room temperature. Once completely cooled, cover the pan tightly with plastic wrap and refrigerate for at least 4 hours, or overnight.
Make the Meringue Topping: In a small saucepan, combine 1 cup + 2 tablespoons granulated sugar, the water, and the corn syrup over medium heat. Bring to a boil, stirring occasionally. Once boiling, do not stir, and heat to 240 degrees F.
Meanwhile, using an electric mixer fitted with a whisk attachment, whip the egg whites on high speed until soft peaks form, about 1 minute. Gradually add the remaining 2 tablespoons of granulated sugar. If the sugar syrup has not yet reached 240 degrees, turn the mixer off and wait. Once the syrup reaches the correct temperature, turn the mixer speed to medium and add the syrup to the bowl in a slow, steady stream down the side of the bowl. Increase the speed to high and beat until thick, fluffy and cool, about 7 minutes.
Spread the meringue on top of the chilled lemon bar, swirling to form peaks. Using a kitchen torch, torch the meringue to a golden brown color. If you do not own a torch, you can place the pan in a 500 degree F oven for a few minutes to brown the top. Be sure to keep a close eye on it so it doesn't burn. Allow the meringue to cool, then slice into bars and serve. Leftovers can be stored in an airtight container in the refrigerator for up to 3 days.