Preheat the oven to 375°F (190°C).
Boil the ziti pasta in salted water until al dente, then drain and set aside.
In a large skillet, warm the olive oil over medium heat and sauté the chopped onion until soft and translucent, about 5 minutes.
Add the minced garlic and cook for an additional minute until fragrant.
Introduce the ground turkey or sausage, breaking it up with a spatula, and cook until browned, about 6-8 minutes. Drain excess fat if necessary.
Pour in the diced tomatoes, oregano, thyme, crushed red pepper, salt, and pepper. Simmer for about 10 minutes, stirring occasionally.
In a separate bowl, blend the ricotta cheese with the egg, adding salt and pepper for seasoning until creamy and smooth.
In a large baking dish, spread a layer of the meat sauce on the bottom.
Layer half of the ziti over the sauce, followed by half of the ricotta mixture, and half of the provolone cheese.
Repeat the layering process with the remaining ingredients, finishing with provolone and Pecorino Romano cheese on top.
Cover with aluminum foil and bake for 25 minutes.
Remove the foil and bake for another 15 minutes until the cheese is melted, bubbly, and golden brown.
Allow to rest for 5-10 minutes before serving and garnish with fresh parsley if desired.