In a large pan, melt the butter at medium heat (be careful not to burn it), add the flour and whisk until it becomes a thick paste.
After a few seconds, add the milk and keep whisking until the milk starts to simmer. Turn the heat to low and slowly keep whisking until the roux it's completely melted and the sauce starts to thicken.
When the sauce is thick enough to coat a spoon, season with salt, pepper and a pinch of nutmeg to taste. Remove from heat and set aside.
Cook the Vegetables
In a large pan, drizzle some olive oil and add the garlic, the thyme and the mushrooms. Sautè for about 10 minutes, until browned.
Add the red wine and let it evaporate, then season with salt and black pepper to taste. Add a few tablespoons of water if necessary and cook until they're soft.
Remove from the pan and set aside to cool down.
In the same pan, drizzle some olive oil and add the zucchini. Sauté for a few minutes, then season with salt and black pepper and add some water to the pan.
Cook until they become translucent. Remove from the pan and set aside to cool down.
Assemble the Lasagna
Pour a couple of tablespoons of white sauce on the bottom of a square 9x9" (23x23cm) baking dish with high borders.
Add a layer of lasagne sheets, another even layer of white sauce, then spread around the vegetables and top with a few chunks of mozzarella.
Repeat for 4-5 layers.
On the top layer, add some more mozzarella and finish with a layer of grated Parmigian Reggiano cheese, to make the crust.
Bake in the preheated oven at 180°C (350°F) for about 40 minutes.