Bring a large pot of salted water to a rolling boil, then add the pasta. Cook until just shy of al dente, about 1 minute less than package instructions. Drain and set aside, reserving a cup of pasta water.
While the pasta cooks, heat a deep skillet over medium-low heat and melt the butter. Once melted and bubbling gently, add the minced garlic. Sizzle until fragrant, about 30 seconds, releasing a warm, pungent aroma.
Stir in the chopped spinach a handful at a time, letting each batch wilt down and turn bright green. Cook for 2-3 minutes until spinach is tender and vibrant, filling the kitchen with a fresh, earthy smell.
Pour in the warm heavy cream, stirring to combine. Bring the mixture to a gentle simmer and cook for 3-4 minutes until the sauce begins to thicken slightly, coating the spinach and garlic evenly.
Add the freshly grated Parmesan cheese to the skillet, stirring until melted and the sauce becomes silky and glossy. If the sauce seems too thick, loosen it with a splash of reserved pasta water to achieve a creamy, cohesive texture.
Season with salt, pepper, and a pinch of nutmeg if using. Taste and adjust the seasoning as needed, ensuring the sauce is flavorful and well-balanced.
Add the drained pasta directly into the skillet with the sauce. Toss gently with a wooden spoon to coat each strand evenly, allowing the sauce to cling to the pasta and absorb flavors for 1-2 minutes.
Serve immediately, garnished with extra Parmesan or a drizzle of olive oil if desired, and enjoy the bright, velvety green goodness of this comforting dish.