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Season both sides of the chicken with salt and pepper.
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Place flour and bread crumbs onto two separate plates. Season each plate with salt and pepper.
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In a small bowl, whisk the eggs.
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Dredge chicken fillets in flour, shake off excess, then dip into the bowl with the egg. Let the egg drip off, then dredge the chicken fillets in the bread crumbs, pressing to adhere. Set aside on a plate.
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Preheat a large nonstick skillet over medium-high heat. Once the skillet is hot, add oil and swirl to coat the bottom.
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Add chicken to the skillet; cook until it is cooked through and golden brown, 3-4 minutes per side (working in batches if necessary). Once chicken is done, remove from skillet and place on a paper-towel lined plate.
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Meanwhile, in a large bowl, prepare dressing by whisking together mayonnaise, vinegar, oil, and oregano.
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Add the lettuce, bell peppers, cucumber, and olives to the bowl with the dressing. Toss to combine.
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To serve, divide the chicken and salad between plates. Top with grated Parmesan and enjoy!