Soak porcini mushrooms in 1 cup hot water for 15 minutes. Drain, reserve soaking liquid and set aside.
Cook linguine according to package directions. Drain and set aside.
Heat 2 teaspoons of the oil in a large skillet over medium heat. Add leeks and cook 2 minutes. Add drained porcini mushrooms and shiitake mushrooms and cook 3 to 5 minutes, until soft. Add sage and stir to coat. Add peas, broth and reserved porcini soaking liquid (strain liquid through a paper towel to remove debris) and bring to a simmer. Simmer 5 minutes. Add mixture to linguine, add parsley and toss to combine. Season, to taste, with salt and black pepper. Transfer to a serving platter and, using a vegetable peeler, shave Asiago cheese over top.