How to Make It
Preheat the oven to 425°. Tightly wrap the outside of a 9-inch springform pan with foil and brush the inside with butter. In a pot of salted boiling water, cook the spaghetti until barely al dente; drain.
In a large skillet, heat 2 tablespoons of the olive oil. Add the onion and garlic and cook over moderately high heat, stirring, until sizzling, about 1 minute. Add the mushrooms, season with salt and pepper and cook, stirring occasionally, until browned, 10 to 12 minutes. Scrape into a bowl.
In the same skillet, heat the remaining 1 tablespoon of olive oil. Add the spinach, season with salt and pepper and cook over moderate heat, stirring, until just wilted, about 2 minutes. Scrape into the mushrooms and let cool slightly.
In a large bowl, beat the eggs with the milk. Add the spaghetti, mushroom mixture, 3 cheeses, sage, thyme, 1 1/2 teaspoons of salt and 1 teaspoon of pepper; mix well. Scrape into the prepared pan and smooth the top. Set the pan on a baking sheet and bake for about 35 minutes, until bubbling and the top is golden. Let stand for 15 minutes. Remove the ring, cut the pie into wedges and serve.