In a saucepan, simmer the broth over medium heat.
In a large, deep skillet, heat the EVOO, 2 turns of the pan, and the butter over medium-high heat. Stir in the garlic. Add the spaghetti and toast lightly, about 2 minutes. Add the onion, carrots, zucchini and thyme. Season with salt and pepper, and cook until the vegetables soften, stirring with tongs, about 5 minutes. Add the wine and cook until completely absorbed. Add a few ladlefuls of warm broth and stir the pasta. Keep adding broth a few ladlefuls at a time, letting the liquid absorb before adding more. Stir often, like you would prepare a risotto, until all the liquid is absorbed and the spaghetti is al dente, 12 to 15 minutes.
Stir the cream and cheese into the pasta, remove from the heat and stir for 1 minute longer, until the cheese is melted and creamy. Serve the pasta in shallow bowls, topped with the lemon peel and parsley.