In a large pot, bring water to a boil and cook the pasta according to package instructions. Drain and set aside.
In a skillet, heat the olive oil over medium heat. Add the diced onion and sauté until translucent, about 3-4 minutes.
Add minced garlic to the skillet and cook for an additional 1 minute until fragrant.
Stir in the shredded chicken and frozen mixed vegetables, cooking for another 3-4 minutes until heated through.
Sprinkle the flour over the mixture and stir to combine, cooking for 1-2 minutes.
Gradually pour in the chicken broth and heavy cream, stirring constantly to avoid lumps.
Add thyme, rosemary, salt, and black pepper. Bring the mixture to a simmer, allowing it to thicken for about 5 minutes.
Once thickened, add the cooked pasta to the skillet and mix well to combine all ingredients.
Stir in the shredded cheddar cheese until melted and creamy.
Transfer the mixture to a greased baking dish and bake at 350°F (175°C) for 10-15 minutes until bubbly and slightly golden on top.