Make the béchamel: In a medium saucepan, heat 2 tbsp (30 ml) olive oil over medium heat.
Add the shallot and cook until softened, about 3 minutes.
Stir in the flour and cook, stirring constantly, for another 3 minutes until it forms a smooth paste (like wet sand) but doesn't brown.
Whisk in all the milk at once.
Bring to a simmer, whisking constantly until it begins to thicken.
Reduce heat to low and simmer gently for 10-15 minutes, stirring often, until the sauce is thick and no longer tastes of raw flour.
Season with nutmeg, salt, and pepper.
Remove from heat and stir in ¼ cup of the Parmesan and the fresh herbs.
Prepare for baking: Preheat your oven to 350°F / 175°C. Lightly oil or butter a 2-quart rectangular baking dish.
Assemble the lasagna: Spread a thin layer of béchamel (about ⅓ cup) on the bottom of the dish.
Arrange a single layer of no-boil noodles on top.
Cover the noodles with another ⅓ cup of béchamel, then half of your prepared vegetables, and a sprinkle of about ⅓ cup of Parmesan.
Repeat and finish: Repeat the layers once more: noodles, béchamel, the remaining vegetables, and another ⅓ cup of Parmesan.
Finish with a final layer of noodles, topped with the remaining béchamel and Parmesan. Ensure the top noodles are completely coated in sauce.
Drizzle with 1 tbsp (15 ml) of olive oil, if using.
Bake the lasagna: Cover the dish tightly with aluminum foil, crimping the edges to seal.
Bake for 30-40 minutes, until the noodles are tender and the sauce is bubbling. For a golden-brown top, remove the foil and bake for another 5-10 minutes.
Let the lasagna rest for 5-10 minutes before slicing and serving.