Bring a large pot of generously salted water to a rolling boil. Add the spaghetti or linguine and cook according to package directions until al dente. Before draining, reserve about 1 to 1.5 cups of the starchy pasta water.

Drain the pasta thoroughly and set aside.

While the pasta cooks, heat the olive oil in a large skillet (10-12 inch) over medium-low heat. Add the drained anchovy fillets. Cook, stirring occasionally and pressing the anchovies with the back of a spoon, until they have mostly dissolved into the oil, about 2-3 minutes. This infuses the oil with their rich, savory flavor.

Add the thinly sliced or minced garlic to the skillet. Continue to cook over medium-low heat, stirring frequently, until the garlic turns golden brown and crispy, about 5-7 minutes. Be careful not to burn it, as burnt garlic can taste bitter.

Stir in the red pepper flakes and cook for another 30 seconds until fragrant.

Add the cooked and drained pasta directly into the skillet with the garlic anchovy oil. Immediately add the lemon zest and about half of the lemon juice (start with 1.5 tablespoons), and half of the chopped fresh parsley.

Pour in about 1/2 cup of the reserved pasta water. Toss everything vigorously with tongs, allowing the pasta water and oil to emulsify and create a glossy, flavorful sauce that coats every strand. If the pasta seems dry, add more pasta water, a tablespoon at a time, until the desired consistency is reached.

Taste and adjust seasoning. You likely won't need much extra salt due to the anchovies, but add fresh black pepper and more lemon juice if desired for brightness. Stir in the remaining fresh parsley.

Serve immediately, optionally garnished with grated Parmesan cheese.