Peel and finely chop the onion and garlic. Sauté them over low heat in a saucepan with 2 tablespoon of olive oil until the onion is translucent. Add the tomato puree, sugar, herbs de Provence, salt, and pepper. Let it simmer on low for 20 minutes.

While the tomato sauce simmers, sauté the ground beef in a frying pan with 2 tablespoon of olive oil for 3 to 5 minutes over medium heat. Season with salt and pepper, then mix it into the tomato sauce. Let it simmer together for a few more minutes.

In a saucepan, melt 70 g of butter. Add the flour off the heat and whisk together. Gradually pour in the milk while whisking to avoid lumps. Return to low heat and let it thicken while stirring regularly. Season with salt, pepper, and a pinch of nutmeg.

Preheat the oven to 180°C (356°F). Grease the bottom and sides of a gratin dish with a little melted butter. Place a first layer of lasagna sheets, spread with béchamel, then add a layer of the tomato and beef filling. Sprinkle with grated Gruyère. Repeat until all ingredients are used, ending with a layer of béchamel and grated Parmesan.

Bake the lasagna in the oven for about 45 minutes until the top is golden and gratinated. Check the doneness of the pasta by inserting the tip of a knife.

Let the lasagna rest outside the oven for 5 to 10 minutes to facilitate cutting. Serve in beautiful rectangular portions, accompanied by a green salad.