Preheat your oven to 325° and bring a large pot of water to boil. Once the water is boiling add in a tablespoon of sea salt and cook pasta 2 minutes shy of what is directed on the package. (see notes)
Meanwhile, in a large skillet, add olive oil and heat on medium.
When hot, add in sliced mushrooms and season with a pinch of kosher salt and some freshly ground black pepper. Cook for 8 minutes or until softened, stirring often.
Next, add in spinach until just starting to wilt. Then pour in the garden vegetable ragu, stir and heat until warmed through.
Drain the partially cooked pasta and add to the pot with the sauce, stir to combine.
Spoon half of the vegetable/ pasta mixture into the prepared pan and top with 1/2 of the mozzrella and provelone cheese and sprinkle with 1/4 cup parmesan.
Add the remaining vegetable/pasta mixture and top with the last of the three cheeses.
Bake on the middle rack of your preheated oven for 40 minutes or until bubbly and the cheese is golden brown.
The times for this recipe was based on having the garden vegetable ragu already made. Allow for extra time if making it all in one day. Also, if making the sauce and mostaccioli at once, sauté the mushrooms after the zucchini. Prepare the rest of thes recipe exactly the same, adding the spinach at the end, after the sauce has simmered for 40 to 60 minutes. I suggest adding the pasta to the water once you've poured in the vegetable ragu to the skillet. A good rule of thumb: the sauce can always wait for the pasta, not the other way around otherwise the pasta will stick together.