Bring a large pot of salted water to a boil. Cook pasta according to package directions until al dente. Reserve about 1 cup of pasta water before draining.
While the pasta cooks, heat olive oil and butter in a large skillet over medium heat.
Add the minced garlic and cook for about 1 to 2 minutes, stirring frequently. Be careful not to let it brown.
If using peas, add them to the skillet and cook until heated through. If using spinach, stir it in and cook just until wilted.
Add the drained pasta to the skillet along with the lemon zest and lemon juice. Toss gently to combine.
Add a splash of the reserved pasta water to help create a light sauce. Start with about 1/4 cup and add more if needed.
Stir in the grated Parmesan cheese and toss until everything is coated and glossy. If using chicken, add it now and warm through.
Season with salt and black pepper to taste.
Serve immediately with additional Parmesan and fresh parsley on top.