Heat 3 tablespoons butter in a large cast iron or oven-safe skillet over medium heat until melted and shimmering.
Pat the chicken thighs dry with paper towels and season both sides generously with kosher salt and black pepper.
Add the chicken to the skillet and cook until deeply golden, about 3 to 4 minutes per side; transfer cooked thighs to a plate.
If the skillet is dry, add 1 tablespoon butter or a little oil; add the orzo and stir to coat in the fat.
Stir in the minced garlic and cook, stirring frequently, until the orzo is lightly toasted and fragrant, about 2 to 3 minutes.
Pour in the 32 ounces chicken stock and bring to a boil, then nestle the seared chicken thighs back into the pan with the orzo.
Reduce to a simmer, cover, and cook until the liquid is absorbed and chicken reaches 165°F, about 15 to 20 minutes; check at 12–15 minutes and adjust as needed.
Drizzle the 2 tablespoons melted butter over the finished dish, then top with chopped fresh parsley and grated Parmesan; serve immediately.
