Season the chicken breasts generously with salt and pepper. Heat olive oil in a large skillet over medium-high heat. Add the chicken and cook for about 5–7 minutes on each side until golden brown and fully cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, melt butter over medium heat. Add sliced mushrooms and sauté for about 4–5 minutes until browned and tender. Add minced garlic and dried thyme; cook for another minute until fragrant.
Pour in the Marsala apple vinegar while scraping up any browned bits from the bottom of the skillet. Allow the vinegar to simmer for about 2–3 minutes until it reduces slightly.
Add chicken broth to the skillet and bring to a gentle simmer. Stir in orzo pasta and let it cook for approximately 8–10 minutes until al dente.
Reduce heat to low and stir in heavy cream until creamy. Return the chicken to the skillet to warm through. Adjust seasoning with additional salt and pepper if needed.
Garnish with freshly chopped parsley before serving hot.