Shred the cooked chicken into bite-sized pieces. If starting from scratch, boil or bake the chicken until fully cooked, then shred.
Heat olive oil in a large skillet over medium heat. Add diced onion and sauté for 3-4 minutes until soft. Add minced garlic and cook for 1 minute. Stir in frozen mixed vegetables and cook for 5 minutes until heated through.
Add cream of chicken soup and chicken broth to the skillet. Sprinkle in dried thyme, dried rosemary, salt, and pepper. Stir well and let simmer for 5 minutes.
Add cooked rotini pasta to the skillet and gently mix until coated with the creamy sauce.
Stir in shredded cheddar cheese and milk. Mix until cheese melts and everything is creamy. Cook for another 2-3 minutes until heated through.