Heat olive oil in a large pot or Dutch oven over medium-high heat.
Add the chicken pieces and cook for 5-6 minutes, stirring occasionally, until lightly browned and cooked through. Remove chicken from the pot and set aside.
In the same pot, add diced onion and cook for 3-4 minutes until softened.
Add minced garlic and cook for 1 minute until fragrant.
Stir in the butter and let it melt completely.
Sprinkle the flour over the onions and garlic, stirring constantly for 1-2 minutes to form a roux.
Gradually whisk in the chicken broth and milk, stirring constantly to avoid lumps.
Add dried thyme, dried parsley, salt, and black pepper. Bring the mixture to a gentle boil.
Add the egg noodles to the pot and reduce heat to medium. Cook for 8-10 minutes, stirring occasionally, until noodles are tender.
Return the cooked chicken to the pot and stir to combine.
Stir in the grated Parmesan cheese and cook for an additional 2 minutes until the sauce thickens and is creamy.
Remove from heat and let the dish rest for 2 minutes before serving.