Preheat the oven to 375°F (190°C).
Place the diced potatoes in a large pot and cover with water. Bring to a boil and cook for 10-12 minutes until tender. Drain and set aside.
In a large skillet, heat olive oil over medium heat. Add the diced chicken and cook for 5-7 minutes until no longer pink. Remove chicken from 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 another 1 minute.
Add the butter to the skillet and melt over medium heat. Stir in the flour and cook for 1-2 minutes to form a roux.
Gradually whisk in the chicken broth and milk, stirring constantly until the sauce thickens, about 3-4 minutes.
Remove the skillet from heat and stir in the sour cream, salt, black pepper, dried thyme, and paprika until combined.
Return the cooked chicken to the skillet and add the cooked potatoes and frozen peas. Stir gently to combine all ingredients with the sauce.
Transfer the mixture to a greased 9×13 inch baking dish. Sprinkle the shredded cheddar and mozzarella cheeses evenly over the top.
Bake uncovered in the preheated oven for 25-30 minutes until the casserole is bubbly and the cheese is melted and golden.
Remove from the oven and let rest for 5 minutes before serving.