Bring a large pot of salted water to a rolling boil, then add the pasta and cook until just al dente, about 10 minutes. Drain and set aside, reserving a bit of pasta water.
While the pasta cooks, heat olive oil in a large deep skillet over medium heat. Add the minced garlic and sauté until fragrant, about 30 seconds, until it starts to bubble and smell aromatic.
Quickly toss in the fresh spinach, stirring constantly until it wilts down and turns bright green, about 1 minute. Let excess water evaporate for a few seconds if needed.
Add the cooked pasta to the skillet with the spinach and garlic. Crumble the feta cheese directly over the hot pasta and stir gently to help it melt into a creamy sauce, about 2 minutes. If the sauce is too thick, add a splash of reserved pasta water to loosen it up.
Squeeze the lemon juice over the pasta, then season generously with freshly cracked black pepper. Mix well until everything is glossy and evenly coated.
Remove from heat and give the pasta a final stir. Taste and adjust seasoning if needed. Serve immediately, drizzled with a little extra olive oil if desired, and enjoy the creamy, vibrant flavors.