Preheat oven to 350 degrees.
Roll prepared pie crust dough to a 12-inch circle. Transfer to a 9-inch deep dish pie pan or 10-inch tart pan. Push down carefully on bottom and sides to remove any air pockets. Fold over edges and crimp as needed. Refrigerate for 20 to 30 minutes. Prick bottom of crust with a small fork. Line crust with foil and fill with pie weights. Place on a rimmed baking sheet on the middle rack in the oven and bake for 15 minutes. Remove weights and foil and continue cooking for another 5 to 10 minutes or until crust is lightly browned and crisp on the bottom. Set aside to cool. Leave oven on.
Place the grated zucchini in a dish towel and wring out moisture. Set aside.
Melt 2 tablespoons of the butter in a large skillet over medium heat. Add garlic and mushrooms and cook 7 to 10 minutes, or until the mushrooms are tender and liquid has evaporated. Remove mushroom mixture from pan and set aside to cool a bit; don’t wash out the pan.
In the same large skillet, heat the remaining 1 tablespoon butter and the olive oil over medium heat. Add zucchini, onion and red pepper and cook, stirring occasionally, until vegetables are soft.
Stir in spinach by handfuls and continue cooking, stirring occasionally, until spinach is cooked and all of the moisture has evaporated.
Remove vegetable mixture from heat, place in a strainer and press with back of a spoon to push out moisture. Let sit for 5 minutes in strainer to allow moisture to drain.
Put zucchini mixture back in skillet (or in a mixing bowl) and stir in cooked mushrooms, basil, thyme, ricotta cheese, Cheddar cheese and 3/4 cup of the Parmesan cheese. Season to taste with salt and pepper. Stir in beaten eggs.
Brush bottom of pre-baked pie crust with the Dijon mustard. Spoon vegetable mixture into the crust and spread evenly. Top with tomato slices. Sprinkle remaining Parmesan cheese over the top.
Bake on middle rack in preheated oven until filling is set, around 40 minutes for a deep dish pan and 30 minutes for a shallower tart pan. Let sit for 10 minutes before slicing and serving.