Bring a large pot of generously salted water to a boil. Add spaghetti and cook until al dente according to package directions, usually about 8–10 minutes. Reserve 1 cup of pasta water before draining.

While the pasta cooks, combine olive oil, sliced garlic, and red pepper flakes in a large cold skillet. Place over medium-low heat and cook, stirring occasionally, until garlic turns pale golden and fragrant, about 3–4 minutes. Do not let it brown.

Add 1/2 cup of reserved pasta water to the skillet and bring to a simmer. Add the drained pasta directly to the skillet. Toss vigorously with tongs for 1–2 minutes to coat the strands in the glossy, emulsified sauce; add more pasta water if needed to keep it silky.

Remove from heat. Fold in the parsley, season with salt and pepper to taste. Transfer to a serving bowl, drizzle with a little fresh olive oil, and top with Parmesan and breadcrumbs if desired. Serve immediately.