Prepare the chicken by shredding it into bite-sized pieces if using leftover chicken or cook it until fully cooked and then shred.
In a large skillet, heat the olive oil over medium heat. Add the diced onion and sauté for about 3-4 minutes until soft. Stir in minced garlic and cook for an additional minute.
Add diced carrots and frozen peas to the skillet and cook for about 5 minutes, stirring occasionally.
Pour in the chicken broth and bring to a gentle simmer. Reduce heat and stir in heavy cream, dried thyme, dried rosemary, salt, and pepper. Cook for another 5 minutes.
Add cooked rotini pasta to the skillet and mix until well coated with the creamy sauce. Stir in shredded chicken.
Stir in shredded cheddar cheese until melted and creamy. Cook for an additional 1-2 minutes and garnish with fresh parsley before serving.