Bring a large pot of salted water to a boil, then add the pasta and cook until just shy of al dente, about 1-2 minutes less than package instructions. Drain and set aside.
Slice the rinsed leeks into thin rings, making sure to rinse out any hidden grit. Chop the mushrooms into bite-sized pieces. Mince the garlic finely.
Heat the large skillet over medium heat and add the olive oil. Once shimmering, add the sliced leeks and sauté for 5-7 minutes, stirring often, until they become soft and translucent, smelling sweet and mild.
Add the sliced mushrooms to the skillet in a single layer. Let them cook undisturbed for about 3-4 minutes until they develop a deep brown color and crispy edges. Stir and continue cooking until the mushrooms release their juices and are caramelized, about 5-7 minutes.
Push the leeks and mushrooms to one side of the skillet. Add a little more olive oil if needed, then add the minced garlic. Cook for about 1 minute until fragrant, the garlic should smell bright and aromatic without burning.
Pour in the heavy cream and stir well to combine, creating a silky sauce. Add the drained pasta to the skillet and toss everything together over low heat for 2-3 minutes, allowing the sauce to coat the pasta evenly and thicken slightly.
Taste the dish and season with salt and freshly ground black pepper as needed. If the sauce is too thick, add a splash of reserved pasta water to loosen it, stirring gently until glossy and smooth.
Remove from heat, sprinkle with chopped parsley, and give it one last toss. Serve immediately, garnished with extra herbs or a drizzle of olive oil if desired.