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Working with one breast at a time, place the palm of your hand on top of the breast and, using a sharp knife, carefully halve the breast horizontally, without cutting all the way through, then open the halved breast like a book. Place the butterflied breast between two pieces of parchment paper or plastic wrap. Pound with the flat side of a meat pounder or rolling pin into a cutlet about ½ inch thick.
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In a shallow bowl, lightly beat the egg with 1 tablespoon water. In a separate large, shallow bowl, combine the breadcrumbs, ground almonds, salt, fennel seeds, and parsley. Dip each cutlet into the egg and let the excess drip off. Place the cutlet into the breadcrumb mixture, turn, and press the breading into the chicken. Transfer to a rimmed baking sheet and repeat with the remaining cutlet.
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In a large skillet over medium-high heat, warm the grapeseed oil until hot, but not smoking. Drop a few breadcrumbs into the oil to test the oil; they should sizzle. Working in batches, place a breaded cutlet into the hot oil and fry until golden, 2 to 3 minutes, then carefully flip and repeat on the second side. Transfer to a clean baking sheet and keep warm.
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In a small saucepan, bring generously salted water to a boil. Add the peas and boil until tender, about 3 minutes for fresh or 30 seconds for frozen. Drain, then rinse under cold water to stop the cooking.
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In a large salad bowl, combine the olive oil, vinegar, green onions, and a generous pinch of salt. Add the lettuce, fennel, and mint. Gently toss together and top with the ricotta salata.
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If the cutlets have cooled too much, reheat them in a 350°F oven for 5 minutes. To serve, place a warm cutlet on a dinner plate and top with a serving of the salad and a lemon wedge.