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1
Pulse bread, 2 tablespoons butter, lemon zest, garlic, 2 tablespoons capers, 1/4 teaspoon salt, and 1/4 teaspoon pepper in food processor until mixture becomes fine crumbs. Transfer to plate.
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2
Place flour in second plate.
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3
Beat eggs in large shallow dish or pie plate.
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4
Pat chicken dry with paper towels and season with salt and pepper. Dredge each cutlet in flour, shaking off excess. Dip in egg, then press into bread crumb mixture to evenly coat. Transfer breaded cutlets to plate and allow to set 5 minutes.
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5
Meanwhile, line baking sheet with 2 layers paper towels. Heat half of oil in large nonstick skillet over medium-high heat until just beginning to smoke. Add remaining 1/4 cup capers and fry until puffed and golden, 2 to 3 minutes. With spatula, transfer to prepared baking sheet.
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6
Add 2 cutlets to now empty skillet and cook until golden, about 3 minutes per side. Transfer to prepared tray.
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7
Discard oil, wipe out skillet, and add remaining oil. Heat until just smoking. Repeat cooking procedure with remaining 2 cutlets.
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8
In large bowl, whisk together yolks, mustard, 1/8 teaspoon salt, 1/8 teaspoon pepper, and lemon juice. In a slow, steady stream, pour in oil while whisking quickly and vigorously until mixture is smooth and creamy.
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9
Discard oil and wipe out skillet. Spread cut sides of rolls with butter. Arrange 2 rolls butter-side down on skillet and toast over medium heat until golden, about 3 minutes. Repeat with remaining rolls.
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10
Arrange one cutlet in each roll, spread with mayo, and sprinkle with fried capers. Serve.
