1. Peel the onion and garlic clove, finely chop them, then sauté them over low heat in a saucepan with 2 tablespoons of olive oil until the onions become slightly translucent.
2. Then add the tomato pulp, sugar, and herbs de Provence. Season with salt and pepper, then let it reduce and simmer over low heat for 20 minutes. While the tomato sauce is cooking, brown the beef in a pan with the remaining olive oil for 3 to 5 minutes over medium heat. Season with salt and pepper, then mix it with the tomato sauce and wait for the cooking to finish.
3. To prepare the béchamel sauce, first melt the butter in a saucepan, then add the flour off the heat and whisk everything together. Add the milk, whisk vigorously to avoid lumps. Place it back on low heat and let it thicken for a few minutes, stirring regularly. Season with salt, pepper, and flavor it with nutmeg.
4. When the filling and béchamel sauce are ready, preheat the oven to 350°F (180°C) while assembling your homemade lasagna. Grease the sides of a gratin dish with melted butter, then place a layer of lasagna sheets on the bottom and spread béchamel sauce over it.
5. Add a layer of filling with tomato sauce and ground beef on top, then sprinkle with grated gruyere cheese. Repeat the process until all the ingredients are used, finishing with a layer of béchamel sauce that you won't forget to cover with a generous layer of grated parmesan.
6. Bake your homemade lasagna for 45 minutes until cooked and golden brown, then let it cool for 5 to 10 minutes before serving in beautiful rectangular portions.