Prepare leeks by cutting off dark green tops and roots. Slice in half lengthwise, fan open layers, and rinse thoroughly under cold water to remove all dirt. Pat dry and slice crosswise into quarter-inch half-moons.

Bring a large pot of salted water to a boil. Add pasta and cook until al dente according to package directions, about 8-10 minutes. Reserve 1 cup of pasta water before draining. Drain pasta and set aside.

While pasta cooks, melt butter in a large skillet over medium heat. Add sliced leeks in an even layer and cook for about 10 minutes, stirring occasionally, until golden brown and very soft. Don't rush this step - the caramelization develops sweet, complex flavor.

Slice mushrooms about quarter-inch thick. Add to skillet with caramelized leeks and increase heat slightly to medium-high. Cook for 5-7 minutes, stirring occasionally, until mushrooms are golden brown and tender. Add minced garlic and cook for 1 minute more, stirring constantly.

Reduce heat to low and pour in heavy cream, stirring to combine. Bring to a gentle simmer, then add grated Gruyere cheese a handful at a time, stirring continuously until each addition melts completely. If sauce seems too thick, add reserved pasta water a few tablespoons at a time.

Add drained pasta to the skillet and toss everything together using tongs or two large spoons until pasta is well-coated with sauce. Season with salt and freshly cracked black pepper to taste. Add more pasta water if needed to reach desired consistency.

Transfer to serving plates or a large platter. Garnish with freshly chopped parsley and serve immediately.