In a large skillet, heat the 2 tablespoons of vegetable oil over medium heat. Add the chopped onion and sauté until it becomes translucent, about 3-4 minutes. Stir in the chopped garlic and cook for an additional minute until fragrant.
Add the 1 pound of ground beef chuck to the skillet, breaking it apart with a wooden spoon. Cook until browned and fully cooked through, about 5-7 minutes. Drain any excess fat.
Stir in the 1 pound of canned tomatoes, 16 ounces of tomato sauce, 1 teaspoon of salt, 1/2 teaspoon of pepper, 1/2 teaspoon of basil, 1/2 teaspoon of oregano, and 2 teaspoons of sugar. Let the mixture simmer for about 15-20 minutes, stirring occasionally.
In a mixing bowl, combine the 1 pound of cottage cheese with 1 egg. Mix well until smooth and creamy. This will be your delicious filling!
Preheat your oven to 375°F (190°C). Meanwhile, cook the 10 ounces of lasagna noodles according to package instructions. Drain and lay them flat on a towel to prevent sticking.
In a 9x13 baking dish, start by spreading a thin layer of the meat sauce at the bottom. Place 3-4 lasagna noodles over the sauce. Spread half of the cottage cheese mixture over the noodles, followed by a layer of mozzarella cheese (about half of the 1/2 pound). Repeat the layers, finishing with a final layer of meat sauce and the remaining mozzarella and Parmesan cheese on top.
Cover the baking dish with aluminum foil and bake for 25 minutes. After that, remove the foil and bake for an additional 15-20 minutes, or until the cheese is bubbly and golden brown. Let it cool for about 10 minutes before slicing.