Heat 2 tablespoons of olive oil and 2 tablespoons of butter in a large skillet over medium heat. Add the sliced leeks, a pinch of salt, and granulated sugar, stirring to combine. Cook for about 20 minutes until golden brown and caramelized.

In the same pan, melt 2 more tablespoons of butter over medium heat. Add the oyster mushrooms and cook for about 8 minutes until browned and tender. Season with salt and black pepper.

Add the minced garlic and sage leaves to the skillet, sautéing for 1 minute until fragrant. Return the caramelized leeks along with the heavy cream, balsamic vinegar, and lemon zest. Simmer for 2 to 3 minutes.

Cook the fettuccine in salted boiling water according to package instructions until al dente, around 8-10 minutes. Reserve 1 cup of pasta water before draining.

Add the drained fettuccine to the skillet with the sauce, reserved pasta water, grated Gruyere cheese, and black pepper. Toss together over low heat until well combined.

Divide the pasta into bowls and garnish with toasted pine nuts. Serve immediately.