Process 1 can of tomatoes with their juices in a food processor until almost smooth, about 5 seconds. Combine the onion, oil, and ½ teaspoon salt in a large nonstick skillet. Cover and cook over medium-low heat until softened, 8 to 10 minutes.

Stir in the garlic, tomato paste, and pepper flakes and cook until the garlic is fragrant, about 30 seconds. Stir in half of the ground turkey and cook, breaking the meat into small pieces with a wooden spoon, until the meat loses its raw color but has not browned, about 4 minutes. Add the pureed tomatoes, remaining can of diced tomatoes with their juices, broth, and bay leaves. Bring to a simmer and cook, stirring occasionally, until the flavors are blended and the sauce is thickened, about 45 minutes.

Stir the remaining turkey into the sauce and continue to simmer, stirring occasionally, until the sauce measures about 6 cups, 20 to 30 minutes. Remove the bay leaves and stir in the basil. Season with salt and pepper to taste.

Mix the ricotta, 2 cups of the mozzarella, Parmesan, basil, egg, salt, and pepper together in a large bowl until thoroughly combined (you should have about 3 cups of filling).

Adjust an oven rack to the middle position and heat the oven to 375 degrees. Spray a 13 by 9-inch baking dish with vegetable oil spray. Spread 1½ cups of the sauce evenly over the bottom of the baking dish.

Lay 3 lasagna noodles on top of the sauce, spaced evenly apart. Place cup of the filling on top of each noodle and spread it out evenly over the entire noodle using a rubber spatula. Spread 1 cup of the sauce evenly over the filling. Repeat this layering twice more.

Lay the remaining 3 noodles over the top. Spread the remaining 1½ cups sauce evenly over the noodles, making sure to cover the edges. Spray a large piece of foil with vegetable oil spray and cover the lasagna tightly.

Place the lasagna on a rimmed baking sheet and bake for 45 minutes. Remove the foil and sprinkle the lasagna evenly with the remaining 1 cup mozzarella. Continue to bake, uncovered, until the cheese is bubbling and slightly brown, 10 to 15 minutes longer. Remove from the oven and cool on a wire rack for at least 15 minutes before serving.