Our cheesy mashup of chicken Parmesan and baked lasagna is towering with layers of crisp chicken cutlets, tomato sauce and three cheeses. We love this dish hot and bubbly right out of the oven, but it is also delicious rewarmed as leftovers. Sprinkle with an extra pinch of Parmesan before serving.
Preheat the oven to 350 degrees F with racks in the center and lowest positions. Put a foil-lined baking sheet on the bottom rack to catch any drips.
Cut each chicken breast lengthwise into thirds, making 9 equal pieces (they should look like large chicken tenders). Put one sheet of plastic wrap on a clean cutting board. Put a piece of chicken in the center of the plastic wrap and top with another sheet. Pound the chicken with flat side of a meat mallet until it is very thin, about 1/4 inch thick. Transfer to a plate and repeat with the remaining chicken.
Whisk together the flour, 2 teaspoons salt, several grinds of black pepper, 1 teaspoon oregano, 1/2 teaspoon granulated garlic and 1/2 teaspoon red pepper flakes if using in a shallow dish until combined. Whisk 3 eggs with 1 tablespoon water in a second shallow dish. Whisk together the panko, 1/2 cup Parmesan, 2 teaspoons salt, the remaining 1 teaspoon oregano, 1/2 teaspoon granulated garlic, and 1/2 teaspoon red pepper flakes if using in a third shallow dish.
Dredge one piece of chicken in the flour mixture, turning to coat evenly. Shake off any excess, then dip into the egg mixture, turning to fully coat. Let the excess egg drip off, then press the chicken firmly into the breadcrumb mixture, turning to coat and packing the crumbs into any crevices. Transfer the chicken to a rimmed baking sheet or large plate and repeat with the remaining chicken cutlets.
Line a clean rimmed baking sheet with paper towels. Heat 2 tablespoons unsalted butter and 2 tablespoons olive oil in a large nonstick skillet over medium-high heat. Add 3 pieces of breaded chicken and cook, flipping once, until the breading is golden-brown and crisp and the chicken is just cooked through, 3 to 5 minutes per side. Transfer to the prepared baking sheet to drain, then season with salt. Wipe the skillet clean and repeat with the remaining butter, olive oil and chicken, making 3 batches total.
Whisk the ricotta, remaining 1 egg, 1/2 teaspoon salt and several grinds of black pepper in a medium bowl until smooth and combined.
Spoon a quarter of the tomato sauce (about 3/4 cup) into the bottom of a 9-inch square baking dish and top with 4 noodles, placing them against the edges of the pan in an even layer (it's ok if they overlap). Spread a third of the ricotta mixture (about 2/3 cup) in an even layer over the noodles and top with 3 pieces of chicken. Sprinkle with 1/2 cup mozzarella and 2 tablespoons Parmesan. Repeat with another 3/4 cup of tomato sauce, 4 noodles, 2/3 cup ricotta, 3 pieces of chicken, 1/2 cup mozzarella and 2 tablespoons Parmesan. Finally, add another 3/4 cup tomato sauce, the remaining 4 noodles, the remaining 2/3 cup ricotta and the remaining 3 pieces of chicken. Top with the remaining 3/4 cup tomato sauce, 1 cup mozzarella and 2 tablespoons Parmesan. (It's ok if the lasagna is slightly higher than the edges of the pan.) Cover the pan tightly with nonstick aluminum foil (see Cook's Note).
Bake until the noodles are tender and the edges are lightly browned, about 30 minutes. Increase the oven temperature to 425 degrees F. Uncover the lasagna and bake until the cheese has completely melted and browned in spots, about 15 minutes more. Let rest for 10 minutes, then cut into squares and serve with an extra sprinkle of Parmesan.
If you don't have nonstick foil, spray regular aluminum foil with nonstick cooking spray before covering the lasagna.
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