How to Make It
Sprinkle chicken with 3⁄4 teaspoon of the salt and 1⁄4 teaspoon of the black pepper. Place flour, eggs, and panko in 3 separate bowls. Stir 1 1⁄4 teaspoons of the salt and 3⁄4 teaspoon of the pepper into flour, and stir remaining 1 teaspoon salt into panko. Dredge chicken in flour, dusting off any excess flour. Dip in eggs, and dredge in panko, pressing lightly to adhere.
Heat 1⁄4 cup of the oil in a large skillet over medium-high until it shimmers. Cook chicken in hot oil, in batches, until chicken is cooked through and golden brown on both sides, about 3 minutes per side, adding remaining 1⁄4 cup oil as needed when skillet begins to get dry. Transfer to a plate lined with paper towels, reserving oil in a heatproof bowl. Keep chicken warm in a 200°F oven. Wipe out skillet with a paper towel, removing any excess panko.
Return skillet to medium-high, and add 2 tablespoons reserved hot oil. Add tomatoes, and cook, stirring occasionally, until blistered on all sides, 3 to 4 minutes. Add capers and white parts of scallions; cook, stirring occasionally, until fragrant, 1 to 2 minutes. Add wine, and cook, stirring occasionally, until sauce starts to thicken, 1 to 2 minutes. Reduce heat to low, add lemon juice and butter, and cook, stirring constantly, until butter melts. Stir in chopped fresh parsley and green parts of scallions; serve immediately with chicken.