For the Bolognese: Heat the oil in a medium skillet over medium heat. Add the pancetta and cook, stirring occasionally, until softened and browned, 2 to 3 minutes. Add the meatball mix with a teaspoon of salt and some pepper. Cook until the meat is no longer pink and has started to crisp up, about 5 minutes. Add the carrots, onions, celery, garlic, 1 teaspoon salt and a few grinds of pepper and cook, stirring occasionally, until the vegetables just start to soften, 3 to 4 minutes. Add the milk, increase the heat to cook down the milk a bit, then add the allspice and tomatoes and stir to combine. Reduce the heat to a simmer and cook until creamy and thickened, 10 to 15 minutes.
Meanwhile, for the Mornay sauce: Melt the butter in a small saucepan over medium-low heat. Add the flour and whisk until a wet sand consistency is formed and smells lightly toasted. Pour in the milk, whisking constantly until thickened and there is no longer a flour taste, about 5 minutes. Add the Parmesan, nutmeg and a few grinds of pepper and whisk until melted and smooth. Season with salt. Remove from the heat until ready to use. (If a film forms on top, whisk vigorously to incorporate it back into the sauce.)
To build the lasagna: Add about 1/4 cup of the Bolognese sauce to a 6-inch oven-safe skillet. Layer 3 lasagna noodle halves on the bottom of the skillet and top with about 1/2 cup of sauce. Repeat until all the noodles have been used. Spoon a final layer sauce on top, then pour over the Mornay sauce being sure to leave a border around the edges. Place the pan on a baking sheet and bake until the noodles are softened and the Mornay sauce is slightly puffed and turning a golden brown, about 15 minutes.