Bring a large pot of salted water to a boil and cook the pasta until just al dente, about 1 minute less than package directions. Drain, reserving about 1 cup of pasta water, and set aside.
While the pasta cooks, mince the garlic cloves until fragrant and slightly golden when sautéed—this releases their aroma and flavor.
Heat the olive oil in a large skillet over medium heat until shimmering and fragrant. Add the minced garlic and cook just until it begins to turn golden, about 30 seconds, filling your kitchen with a warm, savory aroma.
Add the fresh spinach to the skillet. Stir quickly until wilted and bright green, about 1-2 minutes. If using frozen spinach, thaw and squeeze out excess moisture before adding to prevent excess water from diluting the sauce.
Crack in the feta cheese and gently stir to start melting it into the greens and oil, creating a creamy, tangy sauce. Season with salt and freshly ground black pepper to taste. Be mindful of the feta's saltiness as you adjust seasoning.
Add the cooked pasta directly into the skillet. Toss everything together over low heat, allowing the feta to melt into a silky coating that surrounds each piece of pasta, about 2 minutes.
If the sauce appears too thick, slowly add reserved pasta water, a splash at a time, stirring constantly until the sauce reaches a silky, clingy consistency.
Squeeze fresh lemon juice over the pasta and toss gently to brighten the flavors. Taste and adjust seasoning with more pepper or lemon as desired.
Remove from heat and let rest for a minute to allow flavors to meld. Serve immediately, garnished with extra feta or a drizzle of olive oil if you like.