Bring a large pot of salted water to a boil.
Cook the pasta according to the package directions until al dente.
Reserve ¼ cup of the pasta water, then drain the pasta.
Heat the olive oil and butter in a large skillet over medium heat.
Add the garlic and cook for about 30 seconds until fragrant.
Stir in the spinach and cook for 2–3 minutes, until wilted.
Add the cooked pasta, lemon zest, lemon juice, reserved pasta water, salt, pepper, and red pepper flakes.
Toss everything together until well coated.
Stir in the grated Parmesan cheese until melted into a light, creamy sauce.
Remove from the heat and let the pasta rest for 5 minutes to allow the sauce to thicken slightly.
Garnish with chopped parsley and extra Parmesan before serving.