Bring a medium saucepan of salted water to a boil to blanch the peas and a large pot of salted water to boil to cook the pasta. Preheat the broiler.

Toss the asparagus with the oil and 1 teaspoon of the salt. Place in a baking pan under the broiler for 8 minutes, until tender. Slice the asparagus into 1-inch pieces.

Cook each type of pea separately in the boiling water until almost tender, about 2 minutes each. Remove them from the water using a slotted spoon or small strainer. Reserve.

Cook the pasta in boiling water until tender to the bite, about 10-12 minutes. Drain.

Heat the butter in a saute pan until it begins to turn brown. Add the shitakes and shallots. Saute until the shallots and mushrooms are slightly brown.

Add the asparagus, green peas, snow peas, sugar snap peas, marjoram, pepper, and 1 teaspoon of salt. Heat the vegetables thoroughly.

Toss the pasta with the cooked vegetables and scallions.

Just before serving, place a few shavings of cheese on each portion.