Cook the pasta in salted water according to package directions until al dente. Reserve 1/2 cup of the cooking water, then drain.

While the pasta cooks, season the chicken lightly with salt and pepper. In a large skillet, heat olive oil over medium-high heat. Sear the chicken until browned and cooked through, about 5–7 minutes. Remove from the skillet and set aside.

In the same skillet, add a little more oil if needed and sauté the garlic for about 30 seconds until fragrant. Pour in the chicken broth and bring to a gentle simmer.

Stir in the heavy cream and Parmesan cheese. Let the sauce simmer for 2–3 minutes, until slightly thickened. Season with oregano, salt, pepper, and red pepper flakes if using.

Add the spinach to the sauce, letting it wilt down. Return the chicken to the skillet and toss to coat in the sauce.

Toss the cooked pasta into the skillet, adding a splash of the reserved pasta water if the sauce needs loosening. Mix until everything is well coated.

Taste and adjust seasoning. Serve hot with a little extra Parmesan on top.