In a skillet, heat the olive oil and butter over medium heat. Add the garlic and cook for 30 seconds followed by the spaghetti (break the spaghetti so it will fit in the skillet). Toast the spaghetti for 2 minutes until starting to brown, feel free to turn so that the spaghetti does not burn.
Add the onion, carrots, zucchini and dried thyme to the skillet. Cook for 5 minutes or until vegetables begin to soften. Add the wine to the pan and reduce until its completely absorbed. Add 2 cups of vegetable broth, and stir the pasta. Let the pasta cook, add more broth once the pasta has absorbed the broth. Continue this process until all of the broth is used and the spaghetti is al dente (about 15 minutes).
Stir in the heavy cream, Parmigiano-Reggiano cheese, lemon juice and zest. Lastly, mix in the chopped parsley and salt and pepper to taste. Plate the pasta and enjoy!