Preheat your grill to high heat, around 400°F (200°C). Coat the chicken breasts, red bell peppers, and green onions with olive oil, then sprinkle with kosher salt and black pepper.

Place the chicken and bell peppers on the grill grates. Grill the chicken for about 6 minutes per side until it reaches an internal temperature of 165°F (74°C). Add the green onions to the grill during the last 3 minutes.

In a large pot, bring salted water to a rolling boil. Add the whole grain penne pasta and cook according to the package instructions (around 9-11 minutes) until al dente. Drain thoroughly and set aside.

Thinly slice the grilled chicken breasts and chop the bell peppers into bite-sized pieces. Slice the grilled green onions into smaller sections.

In a medium bowl, whisk together the balsamic vinegar, lemon zest, lemon juice, and minced garlic. Gradually drizzle in the olive oil while whisking to create a smooth vinaigrette. Fold in chopped parsley, seasoning with salt and pepper to taste.

In a large mixing bowl, toss the cooked penne pasta with the prepared vinaigrette. Allow the pasta to sit for about 5 minutes to soak up the flavors. Then add the sliced chicken, chopped bell peppers, green onions, and basil leaves, tossing everything together.

Serve the Grilled Chicken Pasta Salad warm or refrigerate for later. Sprinkle grated Parmesan cheese on top before serving for an extra delicious touch.