Position a rack in the center of the oven and preheat to 350 degrees F. Line a 9-by-13-inch glass baking dish with foil leaving a 2-inch overhang on two sides. Grease the foil and dish with 1 tablespoon butter.
For the lemon bar crust: Pulse 1 1/2 cups flour, 1/3 cup sugar, butter, cornstarch and salt together in a food processor until a dough forms, about 1 minute. Press the dough evenly into the bottom of the prepared pan. Bake until the crust is golden at the edges and pale golden in the center, about 30 minutes. Transfer to a wire rack.
Reduce the oven temperature to 300 degrees F.
For the lemon bar filling: Whisk together the eggs and egg yolks with the remaining 1 2/3 cups sugar and the remaining 1/2 cup flour in a bowl until smooth. Whisk in the lemon juice.
Pour the filling over the warm crust and return to the oven. Bake until the filling is just set, about 30 minutes. Cool the bars, completely, on a wire rack, about 30 minutes.
Meanwhile, for the meringue: Bring a few inches of water to a boil in a large saucepan. Whisk together the sugar, cream of tartar, salt and egg whites in a large bowl that sits comfortable in the saucepan without touching the water. Set the bowl above the boiling water and continue whisking until the mixture is hot to the touch (135 degrees F) and the sugar dissolves, 2 to 3 minutes. Remove from the heat and beat on medium-high speed with an electric mixer until the whites hold soft peaks. Increase the speed to high and continue to beat until the meringue holds stiff, but spreadable peaks. Spread and swirl the meringue on top of the cooled lemon bars.
Preheat the broiler to high. Set the lemon bars under the broiler until the meringue is evenly toasted and golden brown, about 30 seconds. (Alternatively, brown the meringue with a hand torch.) Cut into 24 squares and serve or refrigerate until ready to serve.
When measuring flour, we spoon it into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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