Caramelized Leek and Mushroom Gruyere Pasta (Creamy and Cozy)

Ingredients

• 12 oz (340 g) tagliatelle or fettuccine
• 1 tablespoon kosher salt, for the pasta water
• 1 cup reserved pasta water
• 2 tablespoons unsalted butter
• 1 tablespoon olive oil
• 3 medium leeks, white and pale green parts only, cleaned and thinly sliced
• 1/2 teaspoon fine salt, plus more to taste
• 12 oz (340 g) cremini mushrooms, sliced
• 3 cloves garlic, minced
• 1 teaspoon fresh thyme leaves
• 1/2 cup (120 ml) dry white wine or vegetable broth
• 3/4 cup (180 ml) heavy cream
• 1 1/4 cups (140 g) shredded Gruyere cheese
• 1/2 teaspoon black pepper
• 1 teaspoon lemon zest
• 2 tablespoons chopped parsley, for serving