Preheat your oven to 350 degrees Fahrenheit. Season the chicken breasts with a bit of olive oil and a sprinkling of salt and fresh pepper. Bake on the center rack of the heated oven until the chicken is cooked through. About 25-30 minutes fro thawed, and about 45 for frozen. Set aside. This step can even be done a day ahead of time.
Boil a pot of water and cook the pasta according to package directions. Set aside.
Heat a large sauce pan over medium heat and add a drizzle of 2 tablespoons of olive oil. Add the minced garlic and cook slowly until tender, then add the mushrooms. Cook the mushrooms down slowly until they release their juices and darken, wilting down.
Add the cup of heavy cream to the mushrooms and let simmer for about 5 minutes. Add 2/3 cup of the parmesan and let it slowly melt, stirring frequently so it melts evenly with the cream.
Add the pasta to the mixture, then slowly incorporate the spinach, stirring over heat until it all wilts down. Slice the prepared chicken very thinly and incorporate into the pasta.
Heat a small pan over medium low heat and add the pine nuts. Stir frequently until slightly darkened and toasted.
Sprinkle the remaining 1/3 cup of parmesan over the warm pasta, then the pine nuts. Serve warm.