Sear the chicken. Heat a large skillet with a lid over medium-high heat. Add the olive oil and butter. Season the chicken thighs with salt and pepper and sear in batches for 2–3 minutes per side, until golden brown. Transfer to a plate.

Sauté the aromatics. Reduce the heat to medium, adding another drizzle of oil or pat of butter if needed. Add the shallot and cook for about 5 minutes, until softened. Add the garlic, sun-dried tomatoes, thyme, and Calabrian chiles and cook for another 1–2 minutes.

Deglaze and toast. Pour in the vodka and scrape up any browned bits from the bottom of the skillet. Cook for about 1 minute. Add the tomato paste and orzo and stir until well coated. Toast for about 3 minutes, then stir in the oregano.

Simmer. Pour in the chicken broth and heavy cream. Return the chicken and any accumulated juices to the skillet. Bring to a gentle simmer, cover, and reduce the heat to low. Cook for 10–12 minutes, stirring the orzo occasionally, until the orzo is tender and the chicken is cooked through.

Finish the sauce. Stir in the lemon zest, Pecorino Romano, and spinach. Cook just until the spinach wilts and the cheese melts into the sauce. Add a splash of additional broth if needed to loosen the sauce. Taste and season with salt and pepper.

Serve. Top with additional Pecorino Romano and a drizzle of extra-virgin olive oil. Serve immediately.