You will require a 23 x 29 x 7 cm (9 x 111/2 x 23/4 inch) lasagne dish. Adjust the oven rack to the middle position and preheat the oven to 190°C (375°F/Gas 5).
To make the meat sauce, heat the oil in a large heavy-based frying pan over medium heat. Add the onion and cook, stirring occasionally, until softened but not browned. Add the garlic and cook until fragrant.
Increase the heat to medium–high and add both of the meats and a pinch of salt and pepper. Cook, breaking the meat into small pieces with a wooden spoon, for about 4 minutes, or until the meat loses its raw colour but has not browned.
Add the flour and cook, stirring, for 2 minutes, then pour in the vinegar and stir occasionally until it has almost completely evaporated. Add the sugar, passata and diced tomatoes and allow the sauce to simmer for about 10 minutes, or until it reduces and thickens slightly.
Adjust the seasoning, stir through the basil leaves and set the sauce aside (at this stage, the sauce can be cooled, covered and refrigerated for up to two days, then reheated before assembling the lasagne).
To make the béchamel sauce, melt the butter in a heavy-based saucepan over low–medium heat. Add the flour to the butter and stir constantly over the heat, for 1–2 minutes. Remove the pan from the heat and add the milk all at once, whisking constantly, to avoid any lumps. Return the pan to the heat and continue to whisk constantly, until the sauce boils and thickens. Remove from the heat and season with salt and pepper.
To assemble the lasagne, spread one-quarter of the meat sauce into the base of the lasagne dish. Place three of the lasagne sheets over the sauce. Spread another quarter of the sauce over the lasagne sheets, followed by one-third of the mozzarella.
Continue to layer the lasagne sheets, sauce and mozzarella two more times. Pour the béchamel sauce evenly over the final layer of mozzarella, then sprinkle evenly with Parmesan.
Cook the lasagne for 30 minutes, or until the cheese has browned and the sauce is bubbling. Remove the lasagne from the oven and let it stand at room temperature for 10 minutes before serving.