Melt butter in a large skillet over medium-high heat.
Add cubed chicken and brown for 5-7 minutes until cooked through; remove and set aside.
In the same skillet, add onion, carrots, and celery; sauté for 5 minutes until softened.
Stir in minced garlic and cook for 1 minute until fragrant.
Sprinkle flour over the vegetables and whisk for 1-2 minutes to cook out the raw flour taste.
Gradually whisk in chicken broth and heavy cream, scraping the bottom of the pan to release browned bits.
Simmer for 5-8 minutes until the sauce has thickened.
Return the chicken to the pan and stir in frozen peas and dried thyme.
Cook for an additional 2-3 minutes until peas are heated through.
Season with salt and pepper, garnish with parsley, and serve.