Cook pasta in pot of boiling salted water until just tender but still firm to bite. Drain, reserving 1/2 cup pasta cooking liquid. Return pasta to pot.

Meanwhile, cook pancetta in large nonstick skillet over medium heat until crisp. Using slotted spoon, transfer pancetta to paper towels to drain. Pour off all but 1 tablespoon drippings from skillet. Add asparagus to drippings in skillet; sauté 3 minutes. Add peas, white parts of green onions, and garlic; sauté until vegetables are just tender, about 2 minutes.

Add 1/4 cup pasta cooking liquid, dark green parts of green onions, 1/2 cup Parmesan, cream, olive oil, lemon juice, lemon peel, half of parsley, and half of basil to pasta to vegetables. Cook on medium high until cream is reduced slightly.

Add cream/vegetable mixture to pasta and toss. Add more cooking liquid by tablespoonfuls if needed. Season with salt and freshly ground black pepper.

Transfer to large bowl. Sprinkle pancetta, remaining parsley, and basil over the top. Serve, passing additional Parmesan cheese.