Cut the zucchini into small cubes. Drizzle a pan with olive oil and sauté the zucchini for about 5 minutes, until lightly browned and translucent. Season with salt and black pepper.
Remove the zucchini from the pan and set them aside. In the same pan, drizzle a little bit more of oil and add the garlic and the chopped cremini mushrooms.
Sauté the mushrooms for about 5 minutes until they start to brown, then pour the white wine and let it evaporate completely. Add the spinach and cover with the lid until they are completely thawed. Turn down the heat if necessary.
Add the cream, mix well and season with salt and black pepper. Remove from heat and set aside.
Toss the pasta in a large pot of salted boiling water. Drain it 3-4 minutes before cooking time.
In a large bowl or in the same pot, mix the pasta with the zucchini, mushrooms and spinach. Add the pesto and grated cheese and mix well.
Transfer the pasta into individual cocottes or into a baking dish. Butter the dish before adding the pasta.
Sprinkle abundant Parmigiano cheese on top to get a nice crispy crust and bake in the preheated oven for about 15-20 minutes. Turn on the broiler for a couple of minutes if necessary, to get the crust.
You can prep this in advance and keep the baking dish or cocottes covered with plastic wrap in the fridge a day before baking it.