Bring a large pot of salted water to a boil and cook the spaghetti according to package instructions until al dente. Reserve 1 cup of pasta water before draining, then set the spaghetti aside.

While the pasta cooks, heat olive oil in a large skillet over medium heat. Add the sliced leeks and sauté for 5-6 minutes until softened and slightly golden.

Add the minced garlic to the skillet and cook for another 1-2 minutes, stirring frequently, until fragrant.

Reduce the heat to low and pour the heavy cream into the skillet. Stir in the Parmesan cheese and thyme, mixing until the cheese is melted and the sauce is smooth.

Season the sauce with salt and black pepper to taste, adjusting as needed.

Add the cooked spaghetti to the skillet, tossing to coat the pasta evenly with the creamy leek and garlic sauce. If the sauce is too thick, add small amounts of reserved pasta water until it reaches your desired consistency.

Serve immediately, garnished with fresh parsley if desired.