Bring a large pot of salted water to a boil and cook the pasta according to package directions until al dente. Drain and set aside.
Heat olive oil in a large skillet or Dutch oven over medium-high heat. Add diced chicken and cook until browned and internal temperature reaches 165°F (74°C), approximately 7-9 minutes. Remove chicken and set aside.
In the same skillet, melt butter over medium heat. Add the diced onion and sauté until translucent, about 5 minutes. Stir in the garlic and cook for 60 seconds until fragrant.
Whisk in the all-purpose flour and cook for 2 minutes to create a roux, stirring constantly to prevent burning.
Slowly pour in the chicken broth and heavy cream while whisking continuously to ensure a smooth texture. Bring the mixture to a gentle simmer.
Stir in the frozen peas and carrots, dried thyme, salt, and pepper. Continue to simmer for 5 minutes until the sauce has thickened and vegetables are tender.
Fold the cooked chicken and pasta into the sauce. Toss thoroughly to coat all ingredients evenly.
Garnish with chopped fresh parsley and serve immediately.