Melt the butter in a large pot over medium heat.
Add the chicken and cook for 5 to 6 minutes until lightly browned. Transfer to a plate.
Add the onion, carrots, and celery to the pot. Cook for 4 to 5 minutes until softened.
Stir in the garlic and cook for 30 seconds until fragrant.
Sprinkle the flour over the vegetables and stir continuously for 1 minute.
Gradually whisk in the chicken broth until smooth.
Stir in the heavy cream, milk, dried thyme, dried parsley, salt, and black pepper.
Return the chicken to the pot and simmer for 12 to 15 minutes until the chicken is cooked through and the soup has thickened.
Stir in the frozen peas and cook for 2 to 3 minutes.
Mix in the fresh parsley, taste, and adjust the seasoning if needed before serving.