Heat 3 tablespoons unsalted butter in a large cast-iron or ceramic skillet over medium heat until melted.
Pat the chicken thighs dry with paper towels and season both sides generously with kosher salt and black pepper.
Add the seasoned chicken to the skillet and cook until deeply golden, about 3 to 4 minutes per side. Transfer the chicken 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, then add the minced garlic and cook, stirring often, until the orzo is lightly toasted and fragrant.
Pour the chicken stock into the skillet with the orzo, then nestle the cooked chicken thighs back into the pan.
Bring to a boil, reduce to a simmer, cover, and cook for 15 to 20 minutes, checking at 12–15 minutes; cook until the liquid is absorbed and the chicken reaches an internal temperature of 165°F (74°C).
Drizzle the 2 tablespoons melted butter over the finished dish, then top with chopped fresh parsley and grated parmesan. Serve immediately.