Begin by cooking the penne pasta according to the package instructions until al dente. Drain and set aside.
In a large skillet, heat the olive oil over medium heat. Add the diced chicken and cook for about 5-7 minutes until lightly browned. Remove the chicken from the skillet and set aside.
In the same skillet, add the chopped onion and minced garlic. Sauté for 2-3 minutes until the onion is translucent.
Add mixed vegetables to the skillet and cook for an additional 3-4 minutes.
Return the chicken to the skillet. Add thyme, rosemary, salt, and black pepper. Stir to combine.
Sprinkle the flour over the chicken and vegetables, stirring constantly for about 1 minute to coat.
Gradually pour in the chicken broth while stirring continuously until the mixture thickens.
Stir in the heavy cream and bring to a gentle simmer. Cook for 5 more minutes, allowing the sauce to thicken further.
Add the cooked pasta into the skillet, mixing well until the pasta is evenly coated with the sauce.
Stir in the shredded cheddar cheese until melted and fully incorporated.
Transfer the mixture into a greased baking dish and dot with butter on top.
Bake in a preheated oven at 350°F (175°C) for 15-20 minutes until bubbly and golden on top.