Cook the rotini pasta according to package instructions. Drain and set aside.
In a large skillet, heat olive oil over medium heat. Add the diced chicken, salt, and black pepper. Cook until the chicken is browned and cooked through, about 5-7 minutes.
Add the carrots, peas, onion, and garlic to the skillet. Sauté for an additional 3-4 minutes until the vegetables are tender.
Sprinkle the flour over the chicken and vegetables, stirring to combine. Cook for 1-2 minutes to eliminate the raw flour taste.
Gradually pour in the chicken broth while stirring constantly to avoid lumps. Bring to a simmer and cook for 3-4 minutes until the mixture thickens.
Stir in the heavy cream, thyme, and rosemary. Cook for another 2-3 minutes until the sauce is creamy and heated through.
Add the cooked pasta and cheddar cheese to the skillet, stirring until the cheese is melted and everything is well combined.
Remove from heat and garnish with fresh parsley before serving.