Prepare the noodles according to package instructions until al dente, then drain and set aside.
In a large skillet, heat the olive oil over medium heat. Add minced garlic and sauté for about 30 seconds until fragrant, then add ground beef, cooking until browned.
Stir in crushed tomatoes, oregano, salt, and black pepper. Simmer for 10 minutes, allowing flavors to meld.
Add the fresh spinach to the sauce and cook until wilted, about 2-3 minutes.
In a mixing bowl, combine ricotta cheese, half of the shredded mozzarella, and half of the grated Parmesan.
Preheat the oven to 375°F (190°C).
To assemble, spread a thin layer of the meat sauce on the bottom of a baking dish. Layer 4 noodles on top, followed by half of the ricotta mixture, and one-third of the remaining meat sauce.
Repeat the layering process, adding another 4 noodles, the remaining ricotta mixture, and half of the remaining meat sauce.
Top with the final 4 noodles, the remaining meat sauce, and sprinkle with the remaining mozzarella and Parmesan cheeses.
Cover with aluminum foil and bake for 25 minutes, then uncover and bake for an additional 15 minutes until cheese is bubbly and golden.
Remove from the oven and let it rest for 10-15 minutes before serving.