Heat large covered saucepot of salted water to boiling on high. Add pasta and cook as label directs. Drain pasta, reserving 1/2 cup pasta cooking water. Return pasta and reserved cooking water to saucepot.
Meanwhile, slice green onions; reserve 2 tablespoons sliced dark green tops for garnish. In 12-inch slillet, heat 2 teaspoons oil on medium-high heat until hot. Sprinkle chicken with 1/4 teaspoon salt and 1/4 teaspoon freshly ground black pepper. Add chicken to skillet and cook 7 minutes or until chicken is browned and no longer pink throughout, stirring occasionally. Transfer chicken to medium bowl; set aside.
To same skillet, add remaining 2 teaspoons oil; reduce heat to medium. Add green onoins and garlic, and cook 1 minute, stirring. Add asparagus and red pepper; cook 6-7 minutes or until vegetables are tender-crisp, stirring frequently. Stir in cream, crushed red pepper, and 1/4 teaspoon salt. Heat mixture to boiling on medium-high. Stir in reserved chicken pieces and remove skillet from heat.
To saucepot with pasta and reserved cooking water, add Parmesan, chicken mixture and basil; stir to combine. To serve, spoon into bowls and garnish with reserved dark green onion.