In a small bowl, combine the first 4 ingredients (salad dressing through red pepper). Set aside.
In a large skillet, heat oil over medium-high heat. Season chicken with salt and pepper. Add chicken and cook for 3 minutes on each side or until tender and no longer pink.
Add half the salad dressing mixture to skillet; turn chicken to coat. Transfer chicken to a platter and keep warm.
Add asparagus and carrots to skillet. Cook and stir for 3 to 4 minutes or until asparagus is tender.
Transfer veggies to chicken platter.
Stir remaining salad dressing mixture and add to skillet. Cook for 1 minute, stirring constantly and scraping up browned bits in skillet. Drizzle the salad dressing mixture over the chicken and veggies.
Sprinkle with tomato and Parmesan cheese.