Pat the chicken thighs dry and season both sides liberally with kosher salt and pepper.
Heat 3 tablespoons butter in a large cast iron or ceramic skillet over medium heat until melted and shimmering.
Add the chicken to the skillet and cook until deeply golden, about 3 to 4 minutes per side; transfer the chicken to a plate when done.
If the pan is very dry, add 1 tablespoon butter or a splash of olive oil; add the orzo and stir to coat in the fat.
Add the minced garlic and cook, stirring often, until the orzo is lightly toasted and fragrant, about 1 to 2 minutes.
Pour in the 32 ounces chicken stock and stir, then nestle the seared chicken thighs back into the pan among the orzo.
Bring the mixture to a boil, reduce to a simmer, cover, and cook until the liquid is absorbed and the 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.