Add asparagus to large pot of boiling salted water. Cook until just crisp-tender. Transfer to bowl of cold water using slotted spoon. Cool asparagus slightly and drain. Add pasta to same pot of water and boil until just tender but still firm to bite. Add sugar snap peas and boil 2 minutes. Add asparagus and heat through. Drain well. Return pasta-vegetable mixture to pot. Add oil and toss to coat. Add 1/2 cup cheese. Season with salt and pepper. Serve immediately, passing additional cheese separately.