1
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large egg, beaten
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1/4 cup all-purpose flour
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2 (7-ounce) boneless, skinless chicken breasts, lightly pounded to 3/4-inch-thickness
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1 teaspoon kosher salt
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1/4 teaspoon coarsely ground black pepper
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1/2 cup, plus 2 tablespoons (5 ounces) cold salted cultured butter, cut into pieces, divided
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3 tablespoons olive oil
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1/4 cup fresh lemon juice (from 2 lemons)