Heat olive oil in a large skillet over medium-high heat.
Add the chicken pieces to the skillet and cook for 5-6 minutes, stirring occasionally, until the chicken is cooked through and lightly browned. 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 cook for 1 minute until fragrant.
Pour in the chicken broth and whole milk, then stir to combine.
Add the egg noodles to the skillet, making sure they are submerged in the liquid.
Sprinkle in the dried thyme, dried parsley, salt, and black pepper, then stir well.
Bring the mixture to a boil, then reduce the heat to medium-low and cover the skillet.
Simmer for 10-12 minutes, stirring occasionally, until the noodles are tender and most of the liquid is absorbed.
Stir in the cooked chicken and thawed peas until evenly distributed.
Sprinkle the shredded cheddar and mozzarella cheeses evenly over the top of the skillet.
Cover the skillet again and cook for an additional 3-5 minutes until the cheese is melted and bubbly.
Remove from heat and let the casserole sit for 5 minutes before serving.