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Juice lemons; set juice aside. Preheat oven to 350 degrees.
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Grease 9x13" baking dish; set aside. Place cubed butter, 2 cups flour, brown sugar, powdered sugar and salt in food processor and pulse until dough forms.
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Press dough into baking dish so that it comes up about 1/2 inch on the sides. Bake at 350 degrees for approximately 20 minutes.
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Remove crust from oven; let cool on wire rack.
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While crust is cooling, make filling. Whisk together eggs, sugar, lemon zest, lemon juice and flour.
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Pour filling mixture overtop of crust. Bake 30-35 minutes longer.
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Remove from heat; let bars cool completely. Sprinkle generously with powdered sugar, then slice and serve.