Butter a 9x13 baking pan and line with Parchment, leaving a 3-inch overhang.

In a small saucepan, melt butter over medium-high heat until barely browned in color. Remove pan from heat and pour butter into the bowl of an electric mixer, leaving any burned sediment behind. Transfer butter to refrigerator until solidified. When solidified, remove from refrigerator and let soften slightly.

Transfer bowl to electric mixer fitted with the paddle attachment; beat until butter is smooth. Sift flour, confectioners' sugar, and salt into bowl; mix on low speed until combined.

Transfer dough to prepared pan and press evenly into bottom of the pan using the back of a measuring cup; it should be about 1/4 inch thick. Transfer to refrigerator; chill until firm, about 30 minutes

Preheat oven to 350 degrees. Transfer baking pan to oven and bake until crust is golden brown, about 20 minutes. If crust appears to be browning unevenly, rotate pan.

Meanwhile, whisk together eggs, egg yolks, and salt in a large bowl. In a separate bowl, whisk together flour and sugar. Add lemon juice and zest; whisk to dissolve granulated sugar. Add egg mixture to flour mixture and whisk until well combined.

When the crust is golden brown, pull out oven rack and evenly pour filling mixture directly over hot crust (if crust has finished baking before filling has been made, return crust to oven for a few minutes so that it is hot). If air bubbles appear on the surface, remove them using a kitchen torch held 4 to 5 inches from the surface, moving in a slow even motion. Reduce oven temperature to 300 degrees and bake until center is set, 30 to 40 minutes.

Remove baking pan from oven and transfer to a wire rack. Let lemon bars cool completely before covering and transferring to refrigerator until chilled.

Using a sharp knife dipped in hot water and wiped dry, cut lemon bars into twenty-four 2-inch squares and dust with confectioners' sugar just before serving, if desired.