Heat olive oil in a large deep skillet over medium-high heat.
Add the chicken pieces to the skillet and cook for 5-6 minutes, stirring occasionally, until browned and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the diced onion and cook for 3-4 minutes until softened.
Add the minced garlic and sliced mushrooms to the skillet and cook for an additional 4-5 minutes until mushrooms are tender.
Pour in the chicken broth and whole milk, stirring to combine.
Add the uncooked egg noodles, dried thyme, dried parsley, salt, and black pepper to the skillet. Stir well to distribute the noodles evenly.
Bring the mixture to a boil, then reduce heat to low. Cover the skillet with a lid and simmer for 10-12 minutes, stirring occasionally, until the noodles are tender and most of the liquid is absorbed.
Return the cooked chicken to the skillet and stir to combine with the noodles and sauce.
Sprinkle the shredded cheddar and mozzarella cheese evenly over the top of the casserole.
Cover the skillet again and cook for 3-5 minutes on low heat until the cheese is melted and bubbly.
Remove from heat and let the casserole sit for 2 minutes before serving.