Cook rotini pasta in salted water per the package instructions until al dente. Drain well.
Meanwhile, season chicken pieces with ½ teaspoon garlic salt and pepper. In a grill pan over medium high heat, cook chicken in olive oil until juices run clear, about 6-8 minutes on each side. Adjust depending on thickness. Rest for 5 minutes, then cut into bite size chunks. (Likewise, to grill outside, oil grill grates then grill chicken over medium heat for 8 minutes per side)
In a large bowl, place pasta, chicken, cherry tomatoes, olives, red bell pepper, green bell pepper, red onion, green onion, 2 tablespoon parsley, red pepper flakes and reserved 1 teaspoon garlic salt. Add dressing and basil pesto. Toss until well coated.
Add chevre cheese in chunks. Gently mix through, the pasta.
Place into an airtight container and chill for at least 4 hours or overnight.
Serve garnished with additional 1 tablespoon parsley and Parmesan cheese.