Bring a large pot of salted water to a boil and cook the pasta until al dente according to package instructions. Drain using a colander and set aside.
Heat the olive oil in a large skillet over medium heat, then sauté the minced garlic for about 1 minute until fragrant.
Add the chopped spinach to the skillet and cook for 2–3 minutes until wilted and tender.
Pour in the heavy cream and stir well, then add the Parmesan cheese, lemon juice, and lemon zest if using.
Season the sauce with salt to taste and let it simmer gently for 2–3 minutes until slightly thickened.
Add the cooked pasta to the skillet and toss until evenly coated in the creamy spinach sauce.
Serve warm with extra Parmesan cheese and a sprinkle of lemon zest on top if desired.