Bring a large pot of salted water to a rolling boil and cook the pasta until just al dente, about 8 minutes. Drain, reserving a cup of pasta water, and set aside.
While the pasta cooks, heat a large sauté pan over medium heat and add 1 tablespoon of olive oil. Once shimmering, add the minced garlic and cook until fragrant, about 30 seconds, until you smell a warm, pungent aroma.
Add the fresh spinach to the pan in batches if needed. Stir and cook until wilted, about 2 minutes, until the leaves turn a vibrant dark green and release a faint earthy aroma. If the greens release too much water, increase the heat slightly to evaporate excess moisture.
Pour in the heavy cream and stir gently. Bring it to a gentle simmer, then reduce the heat to low. Let the sauce thicken slightly for 2-3 minutes, coating the spinach evenly, until it looks silky and velvety.
Stir in the grated Parmesan cheese until melted and glossy, creating a cheesy sheen. Add a squeeze of lemon juice and season with salt and pepper to taste, adjusting for balance and brightness.
Add the drained pasta directly into the sauce, tossing with tongs to coat evenly. If the sauce feels too thick, gradually stir in reserved pasta water a tablespoon at a time until it reaches a silky, smooth consistency that coats the noodles beautifully.
Cook everything together for another 1-2 minutes to allow flavors to meld and the pasta to soak up the sauce, resulting in a shiny, vibrant dish. Check for seasoning and adjust with more salt, pepper, or lemon if desired.
Remove from heat, drizzle with a little extra olive oil if desired, and serve immediately. Garnish with additional Parmesan or cracked black pepper for a perfect finish.