Preheat the oven to 375 degrees Fahrenheit (190 degrees Celsius).
Cook the lasagna pasta according to the package instructions, and then drain it.
In a bowl, mix the ricotta cheese with the eggs, and chopped parsley, and season it with salt and pepper to taste.
In a separate pan, heat the olive oil and sauté the chopped onion and minced garlic until they are golden brown. Add the tomato sauce and let it cook over low heat for about 10 minutes.
In a 7.5 x 12-inch baking dish, layer the lasagna pasta, followed by a layer of the ricotta cheese mixture. Then, sprinkle some of the grated Parmesan and mozzarella cheese on top. Repeat this process, alternating between the pasta and cheese, until all ingredients have been used.
Pour the tomato sauce over the top layer of lasagna pasta and sprinkle more grated mozzarella cheese on top.
Cover the baking dish with aluminum foil and bake for 25 minutes. Then, remove the foil and bake for an additional 15 minutes or until the cheese is golden and bubbly.
Let the lasagna cool for a few minutes before serving.