In a large Dutch oven or heavy-bottomed pot, heat the olive oil and butter over medium-high heat. Add the chopped onion, carrots, and celery. Sauté for 5-7 minutes, until they begin to soften. Stir in the minced garlic and cook for another minute until fragrant.

Sprinkle the all-purpose flour over the vegetables. Stir constantly and cook for about 1-2 minutes to cook out the raw flour taste.

While whisking continuously, slowly pour in the chicken broth. Keep whisking to ensure no lumps form. Bring the mixture to a simmer, then stir in the dried thyme, salt, and pepper.

Add the uncooked pasta directly to the pot. Stir well to combine, then bring back to a gentle simmer. Reduce the heat to medium-low, cover, and cook for 10-15 minutes, stirring occasionally, until the pasta is al dente.

Once the pasta is cooked, turn off the heat. Stir in the heavy cream, the cooked shredded chicken, and the frozen peas and corn. Continue to stir until the chicken is heated through and the sauce is smooth and creamy.

Garnish with fresh parsley and serve immediately.