To make the bolognese, heat the vegetable oil over medium-high heat in a large, heavy saucepan. Add the ground beef, along with a couple pinches of salt. Brown the meat well and remove it to a bowl using a slotted spoon.
Add the carrot and onion to the pan and lower the heat to medium-low. Cook until the vegetables begin to soften, about 5 minutes. Add the garlic and cook for another minute. Add the tomato paste and cook for one more minute. Stir in the browned meat.
Stir in the flour and then the red wine, if using. Add the tomatoes, stock and oregano and stir well to combine. Raise the heat and bring the sauce to a simmer. Cover the pan and lower the heat so that the sauce is just simmering. Cook until the meat is tender and the flavors have melded, at least half an hour and up to an hour and a half. (Add more stock or water if the sauce starts to look dry.)
While the sauce is cooking, make the bechamel. In a medium heavy saucepan melt the butter over medium-low heat. Whisk in the flour, and once the mixture starts to bubble cook for another 2 minutes, whisking frequently. Don't let the mixture brown.
Whisk in the milk slowly and raise the heat to bring the mixture to a boil. Lower the heat and keep whisking until the sauce turns thick and smooth, 2 to 3 minutes. Remove the bechamel from the heat, cover and set aside.
Heat the oven to 350 degrees. To assemble the lasagna, spread a couple of tablespoons of the bolognese in the bottom of an 8-by-8-inch square baking dish. Add a layer of lasagna noodles, overlapping them slightly if necessary. Spread 1/3 of the bechamel evenly over the noodles, and then spread 1/4 of the remaining bolognese over that. Add another layer of noodles.
Repeat until you have used all of the bechamel. Add a final layer of noodles and spread the remaining bolognese over the top. Sprinkle the mozzarella evenly over the top of the lasagna. Cover the lasagna with a sheet of parchment paper and then wrap the dish tightly in aluminum foil. Bake for about 40 minutes, until the noodles are just tender (test them by piercing the lasagna with a sharp knife).
Turn the oven up to 425 degrees and remove the foil and the parchment. Return the lasagna to the oven and cook for about 10 minutes, until deeply browned and bubbling. Let the lasagna cool in the pan for 5 to 10 minutes before serving.