Season the chicken breasts generously with salt and pepper on both sides. Heat olive oil in a large 12-inch skillet over medium-high heat until it shimmers slightly. Add the chicken and cook for 5 to 7 minutes per side until golden brown with a nice caramelized crust and the internal temperature reaches 165°F. Remove the chicken to a plate and set aside.

Reduce heat to medium and melt the butter in the same skillet, scraping up any browned bits from the bottom. Add sliced mushrooms and cook for 4 to 5 minutes until they release their moisture and turn golden brown. Toss in the minced garlic and dried thyme, stirring constantly for about 1 minute until fragrant but not burned.

Pour in the Marsala wine and use your spoon to scrape up all those flavorful browned bits stuck to the pan. Let the wine simmer for 2 to 3 minutes until it reduces slightly and the alcohol smell mellows out.

Add chicken broth to the skillet and bring the mixture to a gentle simmer. Stir in the orzo pasta, making sure it's submerged in the liquid. Cook for 8 to 10 minutes, stirring occasionally to prevent sticking, until the orzo is tender but still has a slight bite. Keep an eye on the liquid level as orzo absorbs quite a bit. If it looks dry before the orzo is tender, add broth a quarter cup at a time.

Reduce heat to low and stir in the heavy cream until the sauce becomes smooth and creamy. Slice the cooked chicken into half-inch thick strips and return it to the skillet, nestling it into the orzo to warm through for 2 to 3 minutes. Taste and adjust seasoning with additional salt and pepper if needed. Garnish with fresh chopped parsley before serving hot.