Bring a large pot of water to a boil. Salt the water generously — it should taste like broth.
Add the pasta and cook until al dente according to package instructions. Reserve about 1 cup of pasta water before draining.
While the pasta cooks, thinly slice the garlic and finely chop the parsley.
In a large sauté pan over low heat, add the olive oil, sliced garlic, parsley stems, anchovy fillets (if using), and a pinch of red pepper flakes.
Cook gently until the garlic becomes fragrant and lightly golden. Do not allow it to brown.
Add a ladle of reserved pasta water to the pan and allow it to simmer.
Transfer the pasta directly into the sauté pan and toss vigorously to combine.
The olive oil and pasta water will emulsify into a glossy sauce. Add more pasta water as needed to loosen the sauce.
Finish with freshly chopped parsley and toss again.
Serve immediately.