Preheat the oven to 180°C (350°F).
In a large skillet, heat olive oil and sauté onion and garlic until soft.
Add the ground beef and cook until browned. Stir in tomato paste, crushed tomatoes, broth, oregano, basil, salt, and pepper. Let it simmer for 20 minutes.
Meanwhile, melt butter in a saucepan. Whisk in flour, then gradually add milk while stirring until smooth and thickened to make the béchamel sauce.
In a baking dish, spread a thin layer of meat sauce, then a layer of lasagne sheets, followed by béchamel and cheese. Repeat until all ingredients are used, ending with cheese on top.
Bake for 35–40 minutes, until golden and bubbly. Let it rest for 10 minutes before serving.