Gather the ingredients. Preheat the oven to 350 F.
To make the "pasta," slice the sweet potatoes into thin flat strips reminiscent of sheets of pasta using a mandoline. Place the strips in a bowl, drizzle with a little olive oil and season with salt and pepper.
To make the sauce, heat two tablespoons of oil in a large skillet over medium heat. Add the onions, celery, and carrot. Sauté until slightly softened, about 5 minutes.
Add the ground beef. Cook, stirring occasionally and breaking up until browned, about 5 minutes.
Add the garlic and sauté for about 1-2 minutes more. Add the tomato paste, beef broth, wine (if using), and oregano. Stir to integrate the tomato paste. Season with salt and pepper.
Bring the sauce to a low boil then reduce the heat to a simmer, stirring occasionally.
Meanwhile, prepare the béchamel. Add the butter and flour to a small saucepan over medium heat. Whisk frequently as the butter melts. Cook for 2-3 minutes, stirring.
As you whisk, very slowly add the milk to the saucepan. Whisking constantly, bring the sauce to a boil, then reduce the heat to medium-low. Season with salt and pepper to taste. Continue to cook for about 3 more minutes until the sauce is a little thick like gravy. Remove from heat. If desired, add freshly-grated nutmeg to taste.
Reduce the red sauce further, if necessary, until the thickness of a fresh pasta sauce.
Build the lasagna in an 8 x 8-inch baking pan. Arrange the ingredients in layers, as follows: béchamel, sweet potato, red sauce, and ricotta and Parmesan. Repeat this sequence at least three times, saving some cheese for the top. Top with a layer of the sweet potato. Brush the top slices with a little more olive oil and top with the remainder of the cheese.
Bake for 45 to 60 minutes. To test for doneness, simply insert a butter knife into the lasagna. It should easily penetrate the layers (with the exception of the top layer, which will be a bit chewy and crispy).
Cool a few minutes and serve immediately.