Making the veg:
- Heat oven to 220℃/fan 200℃. Line a large baking sheet with foil and grease lightly with extra-virgin olive oil.
- Add the vegetables to a large bowl. Add the extra-virgin olive oil and toss to coat. Season with sea salt and freshly ground black pepper, add the dried parsley and dried basil and toss to combine.
- Arrange the vegetables in a single layer; it’s alright if they overlap a little. Roast for 20 mins, tossing once halfway through. Transfer the cooked veg to a large bowl and set aside.
Making the sauce:
- Heat the extra-virgin olive oil in a large stockpot or Dutch oven over medium heat. Add the onion, carrot and celery stalks and season with sea salt and some freshly-ground black pepper. Cook, stirring occasionally, until softened, 10 to 12 minutes; you want to gently cook the veg, not brown it.
- Add the garlic and fresh rosemary and cook for 1 minute, stirring constantly.
- Add the tomato purée and cook, stirring frequently, until it begins to darken, 2 to 3 mins.
- Add the crushed tinned tomatoes, season sea salt and some freshly-ground black pepper and stir. Turn the heat up to medium-high and bring to a simmer.
- Reduce the heat to medium-low. Simmer the sauce covered for 10 minutes, then simmer uncovered for 10 minutes. The sauce will thicken but still be a little looser than a traditional tomato sauce; the extra water content compensates for not pre-boiling the lasagna sheets.
- Remove the saucepan from the heat. Add the fresh basil, along with the roasted vegetables; stir to combine.
- Taste and season with sea salt and freshly-ground black pepper; you want the sauce to be a little saltier than a standard pasta sauce to compensate for the fact that we are not pre-boiling the lasagna sheets in salted water.
Making the béchamel:
- While the sauce is cooking, gently bring the milk to a simmer in a large saucepan over medium heat. Once it begins to bubble, remove the saucepan from the heat. Transfer the hot milk to a heatproof jug (facilitates pouring).
- Melt the butter in a large stockpot or saucepan over medium heat. Whisk in the flour and cook for 3 mins, whisking continuously.
- Quickly but carefully whisk in the hot milk and increase the heat to medium-high. Bring the béchamel to a simmer, whisking often. It will begin to thicken. Once it barely starts bubbling—a few small bubbles coming up to the surface—reduce the heat to medium-low and cook, whisking often, until thick and velvety-smooth, around 5 mins.
- Remove the saucepan from the heat and whisk in the Parmigiano Reggiano and nutmeg. Season with sea salt and freshly-ground black pepper, to taste.
Assembling the lasagna:
- Heat the oven to 200℃/fan 180℃. Lightly oil a deep 23 cm x 23 cm baking dish.
- Spread 2 ladlefuls of the veggie-tomato sauce on the base of the dish. Cover with a single layer of lasagna sheets; you will likely need to cut some of the sheets to fill all the gaps. Top with 1 ladleful of béchamel, spreading it over the lasagna sheets in a thin, even layer using the back of a spoon.
- Repeat the layers—veggie-tomato sauce, lasagna sheets, béchamel—until you get to the top of the dish; 4 or 5 layers depending on how deep your dish is. Top the lasagna with the sliced mozzarella.
- Place the lasagna on an baking sheet (to catch spills) and bake for 45 mins or until the pasta is cooked through and the top is browned and crisp around the edges. Let it rest for around 10 mins before serving.