Cook tortellini as directed on package, adding peas during last 4 minutes of cook time. Drain; rinse immediately with cold water. Pat with paper towels to remove moisture.
In 3- or 4-quart clear bowl, layer the lettuce, the carrots, chicken, peas, the tortellini, and bell pepper.
In small bowl, mix mayonnaise, pesto and buttermilk. Spread over peppers; sprinkle with parsley. Cover and refrigerate at least 2 hours until chilled or overnight. Stir just before serving.