Bring a large pot of salted water to a rolling boil and cook the pasta until al dente, about 1 minute less than package instructions. Drain and set aside, reserving a cup of pasta water.
Meanwhile, heat olive oil in a large skillet over medium heat. Add the minced garlic and sauté for about 30 seconds until fragrant and just beginning to turn golden.
Add the fresh spinach to the skillet. Stir and cook until wilted, about 2 minutes, until it shrinks and turns a vibrant green. Remove from heat temporarily.
Pour the heavy cream into the skillet with the spinach and garlic. Bring to a gentle simmer and cook for 2–3 minutes until the sauce slightly thickens and coats the spinach evenly.
Stir in the freshly grated Parmesan cheese and squeeze in lemon juice. Mix until the cheese melts and the sauce becomes silky. If needed, loosen the sauce with a splash of reserved pasta water.
Add the drained pasta to the skillet. Toss gently to coat every piece with the creamy spinach sauce, letting everything heat through for about 1 minute.
Season with salt and pepper to taste. Remove from heat and let sit for a minute to allow flavors to meld.
Serve the creamy spinach pasta hot, garnished with extra Parmesan if desired. Enjoy the bright, velvety, and satisfying flavors in every bite.