Cook the Pasta: Bring a large pot of salted water to a boil. Add the pasta and cook according to the package instructions until al dente. Drain, reserving 1 cup of pasta cooking water. Set aside.

Sauté the Leeks: Heat 1 tablespoon of olive oil in a large skillet over medium heat. Add the sliced leeks and a pinch of salt. Sauté for 10-12 minutes, stirring occasionally, until the leeks are soft and golden brown. Remove the leeks from the skillet and set aside.

Sauté the Mushrooms: In the same skillet, add the remaining tablespoon of olive oil and 1 tablespoon of butter. Add the sliced mushrooms and cook over medium heat for 6-8 minutes, until they release their moisture and become golden brown. Stir in the minced garlic and cook for another minute, until fragrant.

Create the Sauce: Add the heavy cream and vegetable broth to the skillet, stirring to combine. Bring the mixture to a simmer and cook for 5 minutes, allowing the sauce to thicken slightly.

Add the Gruyère: Gradually stir in the shredded Gruyère cheese, a little at a time, until it melts and the sauce becomes smooth. Taste and adjust with salt and pepper if needed.

Combine the Pasta: Add the cooked pasta to the skillet and toss to coat in the creamy sauce. If the sauce is too thick, add a splash of the reserved pasta cooking water to loosen it up. Stir in the caramelized leeks and fresh thyme, and toss to combine.

Serve: Divide the pasta among plates and garnish with fresh parsley, if desired. Serve immediately while hot.