Bring a large pot of salted water to a boil. Add the whole wheat rotini pasta and cook according to package instructions until al dente, about 10-12 minutes.
While the pasta cooks, prepare the chicken breasts by patting them dry with paper towels.
In a small bowl, mix the garlic powder, 1/2 teaspoon salt, and 1/4 teaspoon black pepper. Rub this seasoning evenly over both sides of the chicken breasts.
Heat 1 tablespoon olive oil in a large skillet over medium heat. Add the chicken breasts and cook for 6-7 minutes per side, or until the internal temperature reaches 165°F (74°C) and the chicken is cooked through.
Remove the chicken from the skillet and let it rest for 5 minutes, then dice into bite-sized pieces.
Drain the cooked pasta and rinse under cold water to cool it quickly. Drain well and transfer to a large mixing bowl.
Add the diced chicken, cherry tomatoes, cucumber, shredded carrots, red onion, and chopped parsley to the pasta bowl.
In a separate small bowl, whisk together the Greek yogurt, mayonnaise, lemon juice, Dijon mustard, dried oregano, 1/4 teaspoon salt, and 1/4 teaspoon black pepper until smooth.
Pour the dressing over the pasta mixture and toss gently to combine all ingredients evenly.
Taste and adjust seasoning if needed. Chill the salad in the refrigerator for at least 15 minutes before serving for best flavor.
Serve cold or at room temperature.