Bring a large pot of salted water to a rolling boil, then add your pasta and cook until just al dente, about 1-2 minutes less than package instructions. Drain and set aside, reserving a cup of pasta water.
Heat your skillet over medium heat and add 2 tablespoons of butter. Once melted and fragrant, add the minced garlic and sauté until it releases a nutty aroma, about 30 seconds.
Add the fresh spinach to the skillet, spreading it out evenly. Cook, stirring occasionally, until it wilts and darkens slightly at the edges, about 2-3 minutes, developing a faint smoky aroma.
Push the spinach to the edges of the pan, then add another tablespoon of butter to the center and pour in the heavy cream. Bring the mixture to a gentle simmer, stirring gently, until it thickens slightly and becomes fragrant, about 3-4 minutes.
Stir in the grated Parmesan cheese and lemon zest, letting the cheese melt into the sauce. Season with salt and pepper to taste. If the sauce feels too thick, stir in a splash of the reserved pasta water until it coats the noodles smoothly.
Add the drained pasta to the skillet, tossing gently with tongs to coat each piece evenly in the creamy, smoky spinach sauce. Cook together for another 1-2 minutes to let flavors meld.
Remove from heat and let rest for a minute. Taste and adjust seasoning with more salt, pepper, or lemon zest if desired. The sauce should be silky, the spinach tender with a hint of caramelized flavor, and the pasta perfectly coated.
Serve immediately, garnished with extra Parmesan if you like, and enjoy this rich, smoky, creamy spinach pasta.