Heat 1 tablespoon butter and olive oil in a large deep skillet or Dutch oven over medium-high heat. Season diced chicken with salt, garlic powder, and half the thyme. Cook chicken for 5 minutes until golden and just cooked through. Remove to a plate and set aside.
In the same pan, melt remaining 2 tablespoons butter. Add onion, celery, and carrots. Saute for 5 minutes until softened and onions are translucent. Add minced garlic and cook 1 minute more.
Sprinkle flour over the vegetables and stir to coat, forming a thick paste. Cook for 2 to 3 minutes, stirring constantly, to create a roux and remove the raw flour taste.
Slowly pour in chicken broth while whisking to prevent lumps. Add heavy cream and bring to a gentle simmer.
Stir in uncooked orzo pasta, making sure it's submerged. Reduce heat to medium-low, cover, and cook for 12 minutes, stirring occasionally to prevent sticking.
When orzo is tender, stir in cooked chicken, peas, remaining thyme, black pepper, and Parmesan cheese. Heat through for 2 to 3 minutes. If too thick, add a splash of broth; if too loose, let sit uncovered to thicken.
Let rest for 3 minutes before serving. Garnish with fresh parsley and serve warm.