Preheat the oven to 375°F (190°C).
Heat olive oil in a large skillet over medium heat. Add the chicken pieces and cook until lightly browned and cooked through, about 6-8 minutes. Remove chicken from skillet and set aside.
In the same skillet, add chopped onion and cook until translucent, about 3-4 minutes.
Add minced garlic and sliced mushrooms to the skillet and cook until mushrooms are softened and any liquid has evaporated, about 5 minutes.
Sprinkle the flour over the vegetables and stir well to coat. Cook for 1 minute to remove the raw flour taste.
Slowly whisk in the milk, stirring constantly until the mixture thickens, about 3-4 minutes.
Remove the skillet from heat and stir in sour cream, dried thyme, salt, black pepper, and shredded cheddar cheese until the cheese melts and the sauce is creamy.
Return the cooked chicken and frozen peas to the skillet and stir to combine evenly with the sauce and vegetables.
Transfer the mixture to a greased 9×13 inch baking dish.
In a small bowl, combine the breadcrumbs, melted butter, and chopped fresh parsley. Sprinkle this mixture evenly over the casserole.
Bake in the preheated oven for 20-25 minutes or until the top is golden brown and the casserole is bubbling.
Remove from oven and let rest for 5 minutes before serving.