Place the frozen peas in a colander. Cook the pasta in a large pot of salted boiling water according to package directions, adding the broccoli florets during the final 30 seconds. Drain over the peas (the hot water thaws them instantly), then rinse everything under cold water until cool. Set aside.
In a large bowl, combine the cooled pasta, broccoli, peas, red bell pepper, cucumber, and green onions. Add any protein (rotisserie chicken, cooked shrimp, or drained tuna) at this stage if using.
In a separate small bowl, whisk together the mayonnaise, lemon juice, basil, garlic, sugar, ½ teaspoon salt, and ¼ teaspoon pepper.
Pour about half the dressing over the salad and toss gently to coat. Taste and adjust seasoning. Cover and refrigerate for at least 2 hours, or overnight. Store the remaining dressing separately in the refrigerator.
Just before serving, add the reserved dressing and toss to combine. The pasta absorbs dressing as it chills, so this second addition is what keeps the salad creamy. Taste, adjust seasoning, and garnish with fresh parsley if desired.