Heat olive oil in a large deep skillet or sauté pan over medium heat.
Add the chicken pieces and cook for 5-7 minutes, stirring occasionally, until the chicken is browned and cooked through. Remove the chicken from the pan and set aside.
In the same pan, add the diced onion, minced garlic, sliced mushrooms, diced carrot, and diced celery. Cook for 5-6 minutes until the vegetables are softened.
Sprinkle the flour over the vegetables and stir well to coat. Cook for 1-2 minutes to remove the raw flour taste.
Gradually pour in the chicken broth while stirring continuously to avoid lumps.
Add the milk, dried thyme, salt, and black pepper. Stir well and bring the mixture to a gentle simmer.
Cook the sauce for 5-7 minutes, stirring frequently, until it thickens.
Return the cooked chicken to the pan and add the frozen peas. Stir to combine and cook for an additional 3-4 minutes until heated through.
Sprinkle the shredded cheddar cheese evenly over the casserole. Cover the pan with a lid and let it sit for 2-3 minutes off the heat to allow the cheese to melt.
Serve the stove top chicken casserole hot.