Cook the pasta according to directions on the package.
Heat a large sauté pan over medium heat and add about 2 tablespoons of the oil to the pan. Place the mushroom in the pan to sauté and caramelize about 5-7 minutes. Add the tomatoes, sweet peas and spinach and toss a couple of times, then adding the pasta when it is al-dente. Add another 2-3 tablespoons of oil at this point, season and serve with Asiago sprinkled on top.