Cook the pasta according to package instructions until al dente. Drain and set aside, reserving ½ cup of the pasta water.
In a large skillet, heat the olive oil over medium heat. Add the sliced leeks and cook for about 5 minutes, stirring occasionally, until they start to soften.
Add the sliced mushrooms to the skillet and continue to cook for another 5-7 minutes, until the mushrooms are browned and the leeks are caramelized.
Stir in the minced garlic and thyme, cooking for an additional minute until fragrant.
Lower the heat and pour in the heavy cream, stirring to combine. Allow it to simmer for 2-3 minutes until slightly thickened.
Add the cooked pasta to the skillet, tossing to coat in the creamy mixture. If the sauce is too thick, gradually add reserved pasta water until desired consistency is reached.
Remove from heat and stir in the grated Gruyere cheese until melted and creamy. Season with salt and pepper to taste.
Serve immediately, garnished with fresh parsley.